I do enjoy the song "Lighten Up" or is it "Soak up the Sun?" by Sheryl Crow.
In it she sings that she doesn't have "diddley squat." What a wonderful expression!
I don't know how far back it goes, but the phrase was immortalized in a 50's song, I believe,
"My girl is red hot!
Your girl ain't diddley squat!"
Diddley represents a very small amount.
Squat is a verb which means to bend knees in order to almost sit on the floor.....the dictionary says to crouch down or "sit on heels or hams."
It doesn't really add to the meaning of this expression, but I think it's added for emphasis as a short, harsh sounding word.