The short answer is: NO. Unless you have a contractual agreement with the employer, the employer can terminate the employment relationship for any reason except for an unlawful one (e.g. on the basis of gender or race etc.).
The short answer is "Yes, your employer can fire you for that reason." An employer can terminate the employment relationship (absent a contract or CBA) for any reason except an unlawful one (examples of unlawful reasons include termination based on gender or race, etc.). Your employer didn't have to provide any reason at all, but since it did, terminating your employment citing a suspended license is not unlawful.
California is an at-will employment state. An employer can terminate you for a good reason, a bad reason, or no reasons at all. However, your employer cannot terminate you for an unlawful reason (for example on the basis of your race, gender, sexual orientation etc.). Unless you can identify an unlawful reason for your termination, then your employer was entitled to terminate you, even if the reason was untrue.
You can file a wage claim through an administrative process offered by the Department Labor Standard Enforcement (DLSE). There are forms on the website. It's a fairly easy process. http://www.dir.ca.gov/dlse/howtofilewageclaim.htm
Absent a written contract your employer has the same right to fire you that you have to quit. They do not have to give notice or give you a compelling reason for letting you go (just so long as the reason is not unlawful--like your age or sex or race). Sorry to be the bearer of bad news but it doesn't sound like your employer has done anything unlawful.
Unless you have a contractual agreement with your employer they are entitled to direct where you work. Employment in California, absent contractual agreement, is at-will, which means that you are not obligated to travel to work, but your employer is also not obligated to continue the employment relationship.
An employer violates California laws if he or she harasses or discriminates against employees on the basis of a protected class. An employee's race is one such protected class. It would be a good idea to consult with an attorney to discuss potential steps for getting your boss to stop.
I agree with my colleagues above. In California an employer can terminate an employee for a good reason, a bad reason, or no reason at all--just not an illegal reason (i.e. discrimination based on a protected class etc.)
It sounds like your former employer is claiming that you never entered into a lease for the unit you were living in, but that you were extended only a license to use the unit as part of your employment. Landlord tenant laws generally do not apply to licenses. This area of law can be fairly complex, however,and there are sometimes exceptions to this general rule that can be found in local ordinances or other regulations. You should speak to an experienced attorney who deals with landlord-...