Without legal permission to work in the U.S., you will find it extraordinarily difficult to find reputable employment.
I would counsel against illegal employment -- when I was young and stupid I worked on a cash basis for a man who "didn't want none of that OSHA paperwork nonsense", and I was forced to quit the job after he threw a 20 lb. pipe at my head. (Cleaning oil pipeline components with a toothbrush is, by the way, every bit as fun as it sounds.)