hanged to go from alive to dead, as consensus (ooh, I've used that twice today!)
hung if its state of living hasn't changed. (pictures, like a donkey, meat etc)
hung, drawn and quatered is techincally incorrect, as the hanging part killed them, then their corspes were drawn on and chopped into 4 (down and then across). the hung part came because of ease of saying it, but offically, the judge would have said Hanged, drawn and quartered.
so, if you killed the animal by hanging, then it was hanged, and if you put it on a hook after it was already dead, then it was hung.