Hi. I recently moved to NJ but still work in NY. Can NY still garnish my wages from owed taxes even though I live in NJ?

Yes.
Read Your U.S. Tax Return: Working in two or more states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

Absolutely.

In fact, if you owed taxes to, say, California, and they had a reciprocity agreement with NJ, then NJ would garnish your wages on California's behalf to collect the back-due California taxes.