Aw, he's a real cutie :-) You're great for taking him in! I agree that he's probably stressed with being in a strange place and with enforced contact with strange animals, so he probably isn't using a litterbox the way he otherwise would. If you have a smallish room he can have as his own for a day or two, preferably with no carpets or soft furniture and a "shiny" hard floor, he'll probably choose the litterbox when left to himself. I've "homed" cats in a bathroom with success.

He shouldn't be drinking excessively for too long, though.