How to dispose of Fast Food Cups?

Hi, I’m about to start cleaning my room, and I think the main thing worrying me is getting rid of the fast food cups. I have TONS of them, and they all still have some liquid left in them. I can’t get myself to open them, and a lot of them have mold. Any advice on how to get them out? (Also, I live on the second floor, so I have to get them downstairs)