I'm thinking of putting disposable silverware in my room after a party
Why would you need eating utensils in your room
My roommates are nasty people and I don't want to share
Not wanting to share utensils with nasty people is understandable. I think it's fine to keep your personal supply of disposable utensils in your room, so that you don't have to eat after other people.
Yeah, they're gross.
There is no sense in you being miserable. If you don't like your roommates, you should find them a replacement and move out.