The back child support is from being on welfare. And this is from 2 different states.
Social Security Lawyers
You need to consult a famioly law attorney in your state to learn about the statute of limitations on unpaid child support and whether there might be any defenses to the collection of back support. Each state has its own laws concerning collection of unpaid support. For example, in the State of Washington where I practice, each month's support can be collected for up to ten years after the support payment became due. If any of your unpaid support is beyond the statute of limitations, you might be able to obtain a court order reducing the balance of overdue payments.
Child support is the only type of obligation that may result in garnishment of Social Security benefits. The ability of the state (or of the other parent) to garnish your Social Security checks does not have anything to do with the age of the child. Rather, it has to do with the amount owing for support and the state's laws concerning collection of back support. In effect, if your were working and your wages could be garnished for back child support, then your Social Security benefits are subject to being garnished.
Family Law Attorney
Many questions -- you do not state whether the sums being sought are actually owed and were calculated correctly, or where they accrued. As the other lawyer pointed out, all that makes a difference. As to Nevada law (although from your description I think the sums accrued elsewhere), there is no statute of limitations for sums accruing after July 1, 1981. Figure out where the underlying obligation accrued, and consult a lawyer THERE -- if Nevada is only enforcing the obligation, there is little that could be done here. For background, see:
Once you figure out which state is most involved, you should probably seek consultation with an appropriate family law specialist. I would suggest starting your search with the American Academy of Matrimonial Lawyers, which can be viewed at http://www.aaml.org. Good luck.