I recently saw a documentary on The History Channel over here in the states about the early new york gangs, namely the irish(mafia), and made a few references on this song. Actually, it was called 'Paddy Whacked', and stirred up some curiosity in me.
After a little research, and talking to my grandmother a bit, i found out Patty was also slang for a woman on their period. I'm not really sure if these are related, but paddy is definatly meant, or at least was 50 years ago, as an insult to someone with a short temper. By the way, the irish themselves started the nickname Paddy. Take a look at St Patricks Day's 'The wearing of the Green'.
As far as the word Whack, this is still used today as meaning hitting, but was also used for a while by the original new york gangs as a hit(assassination).
The word knick-knack started in the early 1900's meaning poor street performance, and later adopted the meaning 'something worthless'. We still use it to describe really cheap decorative items.
As far as the saying 'give a dog a bone' goes, the only kind of definition i could find on this saying is meaning 'Give me a break', or 'help me out here', a couple other uses of the saying is 'throw me a bone', or 'throw the dog a bone', but it could literally mean as it says. I dont know if these are related at all, but when the definitions of the old slang words are put together, it seems a little too coincidental to be just nonsense.
Thought i would post the info i found on the topic, someone might find it interesting. Atleast this Irish thought it was.