If a 17 year old has moved out of the house, then caught underage drinking who is responsible?

You may be underage but still responsible for your actions. The person who is drinking is responsible, particularly if they knew it was an alcoholic beverage. Other parties may also be involved but would be charged differently.

ANY question on law needs to include your general locale as laws vary by area. In most places a parent is responsible for a child until they turn 18. So the parents could be held responsible for any actions of their children.