If house was awarded to my ex in divorce and my ex never removed my name from house, can I be sued for anything on the house?

There is no doubt you will be sued if there is a law suit. A defense can be developed to remove your liability, but there is not a guarantee you can get out of the case. This is a very sticky legal issue. More specific facts need to be discussed but generally speaking you do have a defense IF YOU ARE PROPERLY REPRESENTED IN COURT. When you are dealing with fragile economic issues in court, competent legal representation should always be sought, as the subject matter of the litigation is so very important. One mistake here could cause the biggest adverse consequence of your life!