1. Rambling can mean several things, but in this song, it means "wandering" or moving aimlessly.
2. "There's none so rare" suggests that these people are "one of a kind" (special and unique).
3. "On the tear" is an idiom and it means that you're behaving energetically. It often describes someone who is engaging in a series of deviant acts (drinking, using drugs, being abusive to people).