Lyric discussion by cassiusitsover 

Cover art for Song of Joy lyrics by Nick Cave and the Bad Seeds

The narrator was definitely the killer, and as far as I can see there's three clear indications of that provided: firstly, the echo of the early reference to his tale of murder befalling "a man and his family" in the question "are you a family man?" Secondly, there's the fact that the narrator quotes Milton, as others have pointed out, fitting the killer's MO, and finally and most eeriely there's the narrator's subtly but distinctly too-knowing description of the details of the murder ("those lunatic eyes, the hungry kitchen-knife").

Brilliant song, gives you a crawling sense of terror and foreboding without ever hammering it's point home clearly.