How do one get straight, vertical lines when photographing furniture or objects on a table from an elevated viewpoint? I want to have the walls and the furniture in the background straight, but at the same time "look down" on my objects so I see more of them. Can it be corrected in Photoshop or do I need a tilt-shift-lens?
You can do perspective correction in PS, an easy way is for example via Camera Raw, or the Distort/Lens Correction filter.
Another method to retain straight verticals while shooting is to shoot with a wide FoV and keep your lens pointed horizontally. Your object will be in the lower part of the image,but you can crop that later (that's why you need the wide FoV). The trick is to not point your camera down to center the chair. (this is basically what a shift lens does, it just saves you the cropping step)
On the software side, it can be corrected in Photoshop. Lightroom even has a panel in the development module dedicated that. There is also software that only does the perspective corrections.
You have to take into account that when correcting the perspective you usually end cropping part of the original photograph. Leave breathing space for the possible crop when taking the picture.
The expensive optical solution is to employ a tilt-shift lens. The advantage opposed to computational solutions is that you retain the full sensor resolution to work with. Whether this results in an actually higher resolution of the result depends on the quality of the optics: after all, the task of spreading out lines for which only short line information is visible is tricky either way. With analog film, optics tended to be the better option but things are not as clearcut digitally.