John, I'm going to be brutally honest here - your biggest problem isn't lack of experience - it's the law school you are attending.
When a law firm looks at hiring new lawyers, one of the first things they look at is the name of the law school.
I'm sure you can learn plenty from the classes you are taking, but the unfortunate reality is that firms want to hire from well-know schools.
The fact that yours is not even ABA approved only makes things worse for you. Sure, you'll be able to take the CA bar. Actually, you could take it now - anyone can take the CA bar. No law school required (and the CA bar exam passage rate reflects this fact - it's extremely low). Do you plan to practice solely in CA?
If you really want to improve your chances of getting a good job, you should seriously consider transferring to a better, fully ABA accredited law school.
As far as experience goes, the traditional course is to do summer internships to gain that experience. Again, you will have an extremely difficult time getting an internship because of the law school you are attending.