Disclaimer: I am not a lawyer. The information below is general in nature and should not be taken as specific legal advice. If you have a specific legal question you should consult an attorney practicing in your jurisdiction that is familiar with the law and case history regarding the issues you wish to address.
The following general information is based on the assumption you are located in the United States or a country with similar intellectual property laws regarding the use and licensing of photographs.
There are a couple of issues involved here that need to be clarified.
- Was there a written contract between your wife and the photographer specifying the allowable use of the images? (In a comment to the OP, you have established there is not.)
- Has the image been used/published publicly in any other way prior to its usage by "The Onion?"
In general, a photographer owns all rights to the images they take unless they sell or assign those rights to others.
If the images were taken in a public place or in a place that is generally accessible to the public the photographer doesn't usually even need the permission of anyone in the image to take the photo and use it for noncommercial purposes.
If the images were taken in a more private venue then the subject needs to give permission for the photographer to take and use the images. In the absence of a written agreement between the photographer and the subject, though, if the subject appears in the images to be posing willingly for the photographer that could be construed as prima facie evidence that the photographer had the permission of the subject until proven otherwise.
The photographer may have published his portfolio to one of any number of social media sites, such as facebook, instagram, twitter, flickr, etc. The user agreements for such social media sites require the user to agree to the terms and conditions of the 'user agreement' before they can join and post on the site. Pretty much all social media sites include language in their user agreement that basically says you give the owner of the site an unrestricted license to use anything you upload and publish on their site: photographs, videos, anything you write, etc. Most of them even reserve the right to assign, transfer, or sell their usage rights of everything posted by the users of their site. In effect, anytime anyone posts a photo to a social media site they've just provided a royalty-free image to the owners of the site and anyone else the owners feel like assigning that right to. The only real limitation is that commercial usage by a third party without a model release will probably not end well for the third party if the pictured individual(s) decide to pursue legal action and have the resources to pursue such a case to the end.
But usage by a satire publication such as 'The Onion' is not usually considered commercial usage unless they use the image in an ad for 'The Onion' or one of its advertisers. Using it in a story is generally covered under either editorial use, artistic use, or fair use as parody. To recover damages from such a publication one generally needs to prove that the usage was both factually false and intentionally malicious and that it caused real measurable harm to the pictured individual. Images of celebrities and other well-known people sometimes carry additional considerations which can give more or less protection to them. So do images of children, physically or mentally disabled individuals, etc. that tend to be more protected than average adults.
Do we have any ground to stand upon to get this removed from the, now various, locations this has been posted?
Maybe. People have gone after satire/parody publications like 'The Onion', 'The National Enquirer', and - my favorite - the long defunct 'Weekly World News'. They've even occasionally won. In most cases the only true winners are the lawyers representing all parties involved.
If you can show that their usage has caused real and measurable damages to your wife, her professional reputation, her business, etc. then you may be able send a "Cease and Desist" letter to get a retraction or public apology, but I wouldn't hold my breath. These types of publications typically feed on the publicity of such controversy. To get any real relief, you're probably going to have to get a high powered attorney and pursue them in a long, protracted legal battle. They'll try to outlast you until you're out of money and other resources and can't continue pursuing the case. If you have a good enough case and can secure the services of an attorney with near limitless resources who cares more about fame and reputation that the cost of pursuing such a case you may be able to ultimately prevail.
Also, if we find out the photographer did in fact sell the photos of my wife without her permission, do we have any claim against him?
Probably not unless you can legally prove that the photographer's usage was in contravention to the agreement which you had with the photographer prior to the production of the images. As the old adage says, "Unwritten agreements are worth less than the paper they are written on."
More in-depth background related to the above answer:
Things like model releases are generally needed to use an image commercially. But the definition of commercial usage may surprise many folks. Just because a photographer, or someone to whom the photographer has assigned rights to an image, sells an image does not automatically make that commercial usage. It is only how the image is actually presented by the user that determines whether the image is used commercially or not. In the united States, commercial usage means that the image is presented in a way that implies that those pictured are endorsing a particular product or service.
Other types of usage that do not present the pictured individuals as endorsing a commercial product or service are NOT considered commercial usage. Even though the purpose of a photographer's portfolio is to show potential clients what kind of images they produce, the actual contents of a portfolio are almost always considered non-commercial usage in the U.S. This is because the subjects pictured in a photographer's portfolio are not assumed to be endorsing the photographer's services. For example, if a photographer is a sports/action specialist their portfolio should contain images of athletes competing in various games. The individuals pictured are there because they are competing in an event that the photographer is shooting. They may not even be aware that their image was taken. Even if they are aware, their primary purpose for being there is to compete, not to assist in soliciting business for the photographer, so there is no implied endorsement.
An image printed in a newspaper along with a story that is related to the image is considered editorial usage. So is an image printed in a history book that illustrates something about history. That is, the image was used in a publication to illustrate a news report or other informative article without attempting to sell or endorse a specific product or service. It doesn't matter at all if the photographer was paid to take the image or not. It doesn't matter at all if the newspaper or history book is distributed free of charge or requires a fee in order to obtain it. It doesn't even matter if there are ads in other places in the newspaper (or book). It only matters what the purpose is of each specific image where that particular image is used. Editorial usage does not require the permission of those pictured in the image as long as the image is factual, isn't intentionally embarrassing (more on that later) and doesn't impinge on a few other considerations.
Some of those considerations would include persons such as incarcerated individuals (the presiding warden or their authorized agent must give permission), school children (the principal or their authorized agent decides), patients receiving medical treatment covered under HIPPA and other health care privacy regulations and statutes, etc. Other considerations would include things with national security implications, such as military bases or research facilities that work on sensitive government projects, as well as places that are specifically covered by federal law, such as federal courtrooms, etc.
There is also artistic usage. Again, it doesn't matter if a book in which an image is included is selling for thousands of dollars, if the image is presented purely for its artistic value and does not imply an endorsement for a product or service then in general it is not considered to be commercial usage. Assuming most of the same limitations for editorial usage, a photographer is free to use an image they own for artistic usage without the consent of pictured individuals if the image was taken in a public place and does not defame or intentionally embarrass those in the image.
In addition to the various ways an image may be used by its owner, there are also ways that an image may be reused by others who don't own rights to the image. This is generally referred to as the fair use doctrine that applies to a wide plethora of different types of intellectual property, such as books, movies, music, etc. as well as photographs. Fair use allows limited usage of copyrighted IP without the permission of the owner for things such as critique, review, news reporting, teaching, and research purposes. Oh, and there's one more thing covered under fair use: parody.
In order to be considered proper application of the fair use doctrine, there are four factors that must be considered:
- The purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes
- The nature of the copyrighted work
- The amount and substantiality of the portion used in relation to the copyrighted work as a whole
- The effect of the use upon the potential market for or value of the copyrighted work
For more about how these four factors are applied to determine if use of a copyrighted work is covered under fair use, please see: Is this type of photo manipulation still violating copyright law?
Remember what we mentioned above about an image being intentionally embarrassing?
There have been a few cases where photos published without consent of the person in the photo were deemed to have been embarrassing and harmful to the general good name or reputation of the pictured individual while at the same time providing nothing that is newsworthy and in the public interest.
One of the classic cases referenced in all of the photojournalism textbooks is Graham vs. Daily Times-Democrat from 1964. Ms. Graham was exiting a funhouse at a county fair when a photographer from the local newspaper snapped her photo just as she passed over a grate that blew up her dress and exposed her underwear. The paper published the photo with the caption "All's fair in Fair Fun." Even though her face was not visible in the photo, Graham asserted that she was identifiable due to two of her children also appearing next to her. She sued the paper and won damages. The jury in the case found that the photo, though truthful and captured in public, was embarrassing without containing any information of legitimate concern to the public. Had the photo also communicated something the jury found to be of legitimate concern to the public, she would not have been awarded damages.
The State Supreme Court stated in their decision of the appeal:
There is a fertile medium in this field of torts for the production of
conflicts between the right of the individual to be let alone, and the
right of the public to know--the latter concept being crystalized in
our age old concept of freedom of speech and of the press.
There is a mountain of case law in the United States that affirms that the individual's right to privacy must be balanced with the public's right to know about things of public interest - and there are few things that won't interest at least some people!
There is also a mountain of case law that falls on either side of that knife-edged balance. Sometimes the publisher convinces the court that public interest was served. Sometimes the pictured individual convinces the court that the image did not serve any legitimate public interest.
Even a signed release may not be enough for a publisher to avoid paying damages in some instances if a court rules they have misrepresented the person pictured.
In 1969 Eugene "John" Raible signed a model release allowing a Newsweek photographer to take a photo of him in his front yard with his children for a story he was told would be a "patriotic story" about "Middle Americans." When the story ran, Raible's full page image, with all signs of the children cropped out, was placed across the fold from a story with the following large headline: "The Troubled American". The word 'TROUBLED' stretched across the entire page in bold lettering. Underneath the large headline was a more conventional sized headline: "A Special Report on the White Majority."
Throughout the multi-page article, quotes from those interviewed placed in the margins in bold italics said things such as: "You'd better watch out, the common man is standing up"; "We've entered paradise and it looks like the place we just left"; "Many think the blacks live by their own set of rules"; "I really worry about this country"; and "For a few, revolution is the only answer"
Raible sued and ultimately won based on the argument that the headline associated with his pictured placed him in a false light by implying that he was troubled and that he held the views of those interviewed for the story that ran for many pages when, in fact, he was neither interviewed for the story nor held the views expressed in it. The case is Raible vs Newsweek (1972).¹ Notice that it took several years for the case to be disposed in 1972 following the time the story ran in 1969.
In the case of a publication such as "The Onion", they generally argue that usage is within a special category of derivative work known as satire or parody. Such use has been viewed by various courts in the U.S. as falling somewhere between editorial and artistic usage on one side and fair use on the other. There's also a LOT of conflicting case law that has been established in various jurisdictions around the U.S. regarding cases concerned with the fair use of use of images in works of satire or parody. Rulings in one jurisdiction often appear to conflict with rulings in other jurisdictions. Sometimes what appears to be an "8" on a scale of 1-10 goes unpunished and at other times in other jurisdictions what appears to have been a "2" gets slapped with major damages. The only real way to know for sure which way most cases based on a claim of fair use that also involves parody will go is to actually pursue the case and run it through the courts. and the appeals. and the appeals of the appeals. and the retrials ordered by the appeals. and the appeals of the retrials... ad nauseum.
¹ The link is to the initial opinion of the court at the summary hearing for deciding if the case should be dismissed, as the defendant requested, if the court should issue a summary judgement against the defendant, as the plaintiff requested, or if the case should proceed to trial. The court denied both requests for summary judgement and sent the case to trial. The plaintiff ultimately prevailed.