Oogatz, Ugatz etc is from the Italian word Il cazzo, meaning c*ck, not balls. (cazzo is the most common italian curse words btw)

Il cazzo in Sicilian/southern Italian dialect is U cazzu.
U cazzu -> U cazz' -> Oogatz

Same with Oobatz which comes from pazzo = crazy

Allora, Pentangeli said, "Clemenza promised them dick (nothing)"