You could take Amtrak. That's right at the Oakland Coliseum (the new airport connector leads right there), although the only trains that stop there are the Capitol Corridor line. Other options to get you on a train or bus would be at Richmond (you can take BART there) or San Jose.
Amtrak runs a variety of trains and/or buses that can get you to Anaheim. There are many combinations, including Capitol Corridor, the San Joaquin, Coast Starlight, Pacific Surfliner, and various connecting bus services. However, what is the most practical would probably to take BART to Richmond and then a series of trains and buses. However, if you're looking to skip a hotel room, much will depend on when you arrive. Your options are pretty poor if it's late at night. There is one bus (4768) that you can take from Oakland-Jack London Square that leaves at 10 PM and arrives at Los Angeles in the morning, where you can connect to a train.
If you send a private message, maybe I can give you some more concrete answers.