Legal Question in Construction Law in California

Lots. Start with filing a complaint with the Contractors State License Board. Contracting without a written contract is illegal and a license violation. If they are in fact licensed you can make a claim against their bond, which you will find listed in their license record on the CSLB website. If you find they are unlicensed, the CSLB will pursue them for unlicensed contracting, and you can sue them for it which will require them to return all money you paid them, even money they might have actually earned.