Considering the damage the previous owner's kids did in general, I'm glad the carpet was there! The carpet had been peed on by their dog (and possibly kids, after the condition of the bathroom I put nothing past them) in multiple spots, thus the odor.
The living room carpet also smells bad, so I assume it has also been baptized. I also need to paint the ceiling, so the plan is to move everything off the carpet that I can, cover the rest, and paint the ceiling without worrying about drips on the carpet. Then I'll remove the carpet, tack strips, staples, and clean. Probably doing all this this week and next weekend. Cross your fingers.