32 cats? Sounds like your roomie could be considered a hoarder. If that is whats going on it is a pretty serious issue that wouldn't be solved by "removing" the cats. The roomie will most likely just allow another stray to come in and take the place of the cat that is gone. I saw you called animal control, did you tell the the severity of the issue? It seems even if they are not be taking in strays, they may be interested in a hoarder/animal cruelty situation.
Regardless of what happens to the roomie and the cats, you need to build a pen. The cats will kill your birds, that's what cats do. Check Craig's list, many times you can find good size rabbit cages for cheap. You could use one as a temp solution until you build a run.
Good luck, I hope you find a solution soon.