Can I sue if I am not a citizen or I am an undocumented worker? What happens if I was paid off the books?

Citizenship or legal status is of no importance in bringing a lawsuit. Anyone and everyone can bring a lawsuit if they are hurt on the job. You can even bring a lawsuit if you are paid off the books. Being off the books may affect how much money you can recover for lost wages, but this depends on the circumstances of your case.