Free from a difficult situation.
To be in a difficult situation is like hanging "on" a "hook"; to get free of the problem you must get "off the hook".
We've caught you again, but this time you won't get off the hook so easily!" You are "off the hook" when you are no longer responsible for some problematic situation. Example: "We found the guy who stole the money, so we know you didn't do it; you're off the hook." When you get yourself free from a difficult situation you are no longer "on the hook"; you are "off the hook." Example: "You're lucky; it turns out that Dad never heard you come in late last night." Answer: "Great, that means I'm off the hook!