OK.....the guy whose shirt was stuffed with a fish was Joe "Joe Jelly" Giorelli.

Giorelli was one of the Profaci Family hitmen who killed Albert Anastasia. He was later involved in the Gallo/Profaci war, and on August 18, 1961 he went fishing with four friends to Sheepshead Bay. He was never seen alive again, and his shirt, wrapped around a large fish was thrown into the street in front of his hangout. It was clearly a message that he was sleeping with the fishes.

I'll try another question:

Who was the guy that (really) got strangled in a bar (and survived) much like Frankie Pentangeli did in Part II? (Hint - He's from the same era as Giorelli).