The linguistic or artistic reference to beer or any other alcoholic beverage, which is intended to be humorous (i.e. jokes, stories, clothing, music etc.).
A shirt that reads "this is not a beer belly" and points to a man's protruding mid-section: a clear beer-joke.
An unfamiliar fan at a football game is trying to start conversation and tells you a story about how he and his friends use to sneak onto the roof and drink heartily. (The story is told with profanity, laughter and inappropriate gestures): a disquised beer-joke.
You're Uncle offers you a beer at the family reunion even though he knows that you are thirteen years old. He doesn't intend to give you the drink, but simply offers it in order to have a cheap laugh and incite chuckles among other buzzed males: beer-joke of the 1st degree
Any other PRE-MEDITATED joke that involves alcohol: beer-joke of the 3rd degree.