Sounds like you are living next to a hoarder or "pack rat." You mentioned all the clutter and bags of stuff in a room. I've known a few and have been in their homes. Yikes! I've asked what they are doing holding on to the stuff and a typical answer is, "It might come in handy." If your neighbors are pack rats they might be really offended that you tried to clean up their house. If the pets are fed, watered, and healthy (vet checked, tags are up to date, etc), PCA won't be able to do much. Maybe there is a local ordinance regarding the number of pets that are allowable in a household. Its a tough situation. Here's a link that discusses pack rat behaivior:
http://www.findarticles.com/p/articles/mi_m1175/is_n2_v22/ai_6306685
Other posters have given you some pretty good suggestions. Good luck.