I would consider neither the EF 135mm f/2 L nor the EF 70-200mm f/2.8 L IS for that situation. Others will disagree, but that is my preference at a large party where most of the guests are up and moving around. Of the lenses you don't already have available the best candidate for rental would be the Canon EF 24-70mm f/2.8 L II. If your budget can't handle that, then the Tamron SP 24-70mm f/2.8 Di VC. It is a little sharper than the original Canon EF 24-70mm f/2.8 L and also has image stabilization. The other thing I might consider if I were in your shoes would be using the three excellent primes you own and if changing lenses is an issue, then renting a second FF body. But then you'd also need a second E-TTL flash (you don't want to try shooting an event like this with people constantly moving around using manual flash - if they're seated in the same spot most of the time it would be a different story). The problem with the longer focal lengths is three-fold:
The inverse square rule. Your flash loses power exponentially the further away your subject is. At f/2 or f/2.8 in most reception halls/restaurants/banquet rooms you're still going to need flash regardless of the lens you use. I get better results putting a diffuser on the flash, either bouncing it off the ceiling or holding it off camera (with an off-shoe cord and either via bracket or using my left hand), and getting a little closer. The further you are from your subject, the closer to the optical axis your flash will be in angular terms for the same distance it is held from the hot shoe.
Obstructions. Trying to shoot from 15-20 feet so as to not be intrusive sounds like a good idea - until you get in a crowded room with wall to wall people and you can't get a clear view of anyone at that distance without someone else walking between you and the subject(s). And frankly, most people at a party prefer to be given the opportunity to pose and present their best look before the shutter is snapped. That's not to say you shouldn't try to get some candid, unposed shots. But even then, you don't want to catch them stuffing their face with food, swigging a drink, or with their mouth contorted talking to someone - which is mostly what they'll be doing when they aren't posing for you.
Groups. You need a wider angle of view to shoot groups of 3-4 people than you need when shooting individual portraits. Most people attending a party are going to be in groups, not by themselves. For groups of 2-4 people I use focal lengths between 35mm and 50mm the most on a full frame body. Since the subject distance is further than if you were trying to fill the frame with a single person, you won't have issues with facial distortion. Perspective is strictly a function of shooting distance, not focal length as many people believe. To get 3 people in the frame you need to use about 35mm to use the same shooting distance you would use with a 90mm lens shooting an individual.
Even with faster glass, such as your EF 50mm f/1.4 or EF 24mm f/1.4 L, you often can't leverage the wider aperture because you need a deeper depth of field to make sure everyone who may be closer or further away from the camera are properly focused. Those lenses are perfectly usable, but you will need to stop them down a bit to get the depth of field you will likely need.
Forget the 7D in that type of environment. I've got one and it is a good sports camera in decent light, but for events in darker environs, the 5D III is clearly superior in terms of high ISO noise performance, dynamic range, noise, white balance/color accuracy, noise, and noise.
The following were all shot using a Canon 5D II + EF 24-70mm f/2.8 L + 430EXII (w/Stofen Omni-Bounce diffuser). Aperture Priority with Tv limited to 1/200-1/60 sec via C.Fn I-07 (flash sync speed in Av mode) and E-TTL flash mode. Essentially I was shooting manually at 1/60 sec + selected aperture unless the ambient light was too bright (not likely) in which case the Tv would be shortened. The E-TTL flash then added whatever was needed to expose the subject. I adjusted the ISO based on the ambient lighting in the frame. I selected aperture based on desired depth of field. I set Flash Exposure Compensation (FEC) based on distance, subject reflectivity, and the mood desired.
51mm. ISO 1600, 1/60 sec, f/2.8. FEC -1. Flash mounted on hot shoe bounced off ceiling. Cropped from 5616x3744 to 5327x3551 before resizing for web.
24mm. ISO 800, 1/60 sec, f/2.8. FEC -1 1/3. Flash bounced off ceiling. Cropped from 5616x3744 to 4423x3537 before resizing for web.
32mm. ISO 1600, 1/60 sec, f/2.8, FEC -1. Flash hand held ≈24-30 inches left of camera (probably a bit too far). Cropped from 5616x3744 to 4676x3117 before resizing for web.