What to do if my state tax refunds have been garnished for the last 3-4 years for a debt that my husband incurred before we were married?

At this point, your joint income tax returns will be subject to full garnishment because you commingled monies and you probably filed jointly. If this is the case, then you need to discuss the possibility of filing separately and seeing if that will help matters but keep in mind the monies being garnished will still be garnished and it will be still coming out of the marital assets.

By law, creditors may only garnish the assets of the spouse that incurred the debt. In reality, joint assets are often effected by the judgement: joint accounts are garnished, liens on houses owned jointly, etc.  Contact the state attorney general's office regarding having your portion of the refund released.  And the creditor as well.  Good luck.