I just found tweets on my Twitter that I didn't tweet. They're advertising, like "lose 30 lbs in 30 days" or "guess who's stalking you" and so on. What do I do besides change my password?!

Change your password it's all spam and a virus. It's happened to a lot of people on twitter as I keep gettin spam from everyone. At the moment there's nothing you can do. These people will keep on doing this. Nobody has actually hacked your account, they have done it through the computer. Contact twitter if it becomes a problem, twitter actually listen.