sounds like step-dad controls all the finances. you could offer to pay him a small rent to stay there for a while until you can find a new place. say you're sorry for whatever happened in the past to make him dislike you so much.
say you'll also help out with the chores. don't party so much, save a little bit more money so you can leave sooner and get on with your thing. take over some chores you know he hates (like mowing the lawn, I hate it).
that should work.