Firstly, as others stated, you took a risk and likely violated your lease as well as NYC law.

With that said, this tidbit from your listing is a brilliant indicator of how you inevitably brought this issue onto yourself:

"You may host up to 50 people in the backyard or apartment, but please leave $80USD so I can pay a cleaning lady to clean the extra mess."

Did they pay the extra $80USD? You invited them to bring 50 people over, I am sorry for what happened, but I don't feel sorry for you...