Towels would be fine. Just wash them if they get wet. If you clip them up and leave about 1 inch gap above the bedding, they won't get as dirty.
Ah, ok!
Well, after watching the piggies and observing their behaviour, and taking the advice from everyone on here, I think I've managed to strike a balance and figure out the right set-up for them until I can get the new cage. The more I look at them in the small space, the sadder I get, but I truly believe they'll be ok for a little while.
For bedding I've used newspaper and special paper bedding that comes in all colours (my roommate's rabbit didn't like that particular kind so she gave me half a bag, very kindly.)
I have two of everything, as they tend to fight over stuff if I don't: I have two water bottles, two places for hay/pellets when I give them pellets, and two places to hide/sleep that's fully covered. They LOVE their hide-aways, so i figured instead of freeing up the space so they can run, I'll give them both each a place to hide. They seem very attached, and eventually I'll get rid of one of them and make fleece forests, when I have the space. The purple hut was in the corner but they push it out every time I put it in the back and I figured I'd leave it there.
Finally, I put a fleecey-feeling hand towel in the corner, and my one little guy John has zipped under there a few times.
I know this is far too small and I know I'm technically a horrible owner because of that, but I really have no option but to keep them in what their previous owner had them in for almost their whole lives. I'm going to work towards C&C within the month.
And in this picture, you can see my baby piggies sitting, staring at the woman with the camera. They're so cuuuute EEEE.