You can file tax no matter how you get money. Once you get money over 400 dollars you have to file as self employments and you will be ended paying equally the same amount if you were paid over the table job. Now you do not have any withheld either federal or state, if you owe more than 1000 dollars in the cash work while filing tax , will be paying penalty.

Now your question is if you are not filing tax because you do not have w-2 form , is that going to be a problem on your citizenship? I guess it will not. If you have to prove your income for the all years, then think of working over the table.