J. - Oh, I feel your pain, too! The lack of sleep I am sure isn't helping either. I have a strong-willed almost 3 year old who has major sleep issues, too - here's my advice.
1. for the sleep - he may have woken up, but he is still very tired. A battle of wills is just frustrating, as is trying all the mechanisms of forcing him to stay in bed. That forces him, in his strong-willed-ness, to continue the battle no matter what, because he's just hard-wired to be like that. I know you think that "giving in" will set a precedent, and yes, maybe it will, but for now, why not just try it? Try sympathizing with him - when I have done this with my son during his middle-of-the-night freakouts, after a few minutes he settles right down and falls back asleep. In my experience, the middle of the night is the wrong time to continue battles, your goal is to get everyone back to sleep and it doesn't matter how you do it. Now that my son is getting on the north side of 2, he's able to talk with me better and understand consequences. So I am jsut starting to use a reward / punishment system with him for middle of the night stuff. He still doesn't get it, though, and I don't think this will really work for about another 6 months or so. The maturity isn't there.
2. The general battle of wills. This is the age that kids test the boundaries. They just really want to find out what happens when they defy you. After spending too many hours crying and telling myself I'd never get the hang of parenting, I realized that I don't need to win. Again, my goal is to, say, get out the door in the morning - so when my son refuses to get dressed, I don't engage in it, I simply give him choices - red or blue shirt, Elmo or Thomas shoes, etc. This way he is still getting to make the "decision". This has worked very, very well in almost all areas. I took away the element that we're on opposite sides and gave him a modicum of control. For the strong-willed kid, I think this will almost always work. But when it doesn't, walk away. Punishments like time out or spankings haven't seemed to work for my little guy. They do sometimes (and are necessary for some infractions), but not as a rule when dealing with simple battles, so I try not to think of them as options. This has helped, too. For food - I always serve at least one thing he loves, like croutons, and he starts out with a few, but in order to get more he has to take one bite of something else. I am still surprised that he does this for me each and every time. I am waiting for him to refuse, and then I don't know what I'll do...
My strong-willed son has been very challenging, but once I changed my mindset and realized it's not about me as a parent winning, but instead is about the two of us winning as a team (accomplishing the goal), it freed me up to better relate to him and keeps us both from being unnecessarily frustrated.
I hope this maybe helps you a little bit - just remember you're a team. Sure, you're the leader, but it's okay to let him win sometimes. Lose the battle to win the war...
Good luck!
S.