Long story short, my ex-wife was awarded the house and ended up selling it in a short-sale. The VA says I owe them money. Can I appeal?

The real question is, how your assets were divided in the divorce. If she was awarded the "house" there was probably language about equity or the loan. Bottom line is you are likely on the hook for half that money owed at best.

I did not know that a VA home loan could be awarded to a ex spouse. I went through a divorce and my ex wife tried to get the home. Because the house was a VA Guarantee loan and she was a veteran the only thing that she could do was live in the house until some time when i sold it or she buy me out.

There are many factors surrounding this and you deal directly with your VA service advisor. They do at times work with the veteran surrounding their situation and it would be highly recommended to speak directly with them. Often times in some cases if it is their first loan they will work with you; file your appeal Sir!!