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have they put a lien against your home? They certainly can and can take anything you have in your name.

why don't you use the profit from the home to pay off the arrearages? then the question of how it affects your credit is moot

The effect on your credit will be the same as any other outstanding or delinquent debt.

If you need a loan to purchase another home, you do NOT want this on your credit.

it shows up very badly on your credit. A lot of places will not give you a loan- they consider it kind of like a federal loan- same reason they won't loan to ppl with IRS levies. The gov't can put their lien to the front and take precedent over the other lender. Also, they can take your half. Your spouse would have to file an injured spouse report.
If they say you were served, yet you never saw it- ask to see the proof of service. If you didn't sign for it or they didn't go thru the proper channels to serve by publication, you may be able to knock some off.

If you apply for a new home loan, you will have to pay the back support before closing on your new home.