Should I use a differential mode amplifier for mixing up to four stereo signals together?
I should note that I'm still in the process of designing the whole project, which means that I don't have a power supply chosen, haven't selected volume controls, and don't know what values to use for any of the resistors yet. (yes, I'm asking this question very early in the design process)


This doesn't sound too early at all!

If you have a single-ended input, a differential amplifier won't help anything; AC-coupling (i.e. with a sufficiently large capacitor) to a single-ended amplifier is what you want to do. Hint: through AC coupling, you can bias the audio signal to a half-supply-voltage potential, and that eliminates the need for bipolar power supply for the opamp.

All the sources you describe are single-ended.

Notice that even if you have any differential amplifiers in your system, a single opamp's output is usually single-ended. (There's opamps with differential outputs, but let's call them special-purpose.)


  outputs are going to go to my PC speakers, a pair of headphones, the line-in jack on the PC, and a spare auxiliary output.


Remember that the headphones jack will probably benefit from getting more power than an opamp output can deliver – luckily there's a lot of headphone amplifiers you can choose from. Just stay away from the "every website has a bad example circuit with it" LM386 (it's a thing from the past, and modern amplifier ICs do way, way better).