Very big issue involving cats and our new landlord, what should I do?

If I were you, I'd confront the landlord and be honest. Mention that they have no place to go and your only option is for you to take them in. Most apartment complexes (actually I think all) charge you extra for having pets in the house. But to be honest I had a cat in my apartment and my landlord or manager of the complex never knew nor found out. I find it the right way to be honest because if the landlord were to find the cat and you never told him/her then that's twice the penalty. Just be honest! :) Good luck!