1) the author intended it to be funny (the catalog of “Weird” Al Yankovic)
2) the author did not intend a song to be funny but the song is so over the top that no one takes it seriously (William Shatner doing “Lucy in the Sky With Diamonds”)

The trick with this, of course, is that it depends on knowing the author’s intent. Also, the following characterstics are worth one point each; if a song has more than three points it becomes a novelty song just by attrition:
–having a story that resolves in a twist ending (“Lola”
or “Escape! (the Pina Colada Song)”).
–Unusual subject matter (Yellow submarines, distopian futures in which robots are thanked)
–spoken word(“Thriller” “Everybody’s Free to Wear Sunscreen”)
–a musical “gimmick” (children’s choir, strings, employing an odd vocal style like opera).

There are many popular songs which use one of even two of these features which are not novelty songs. For instance, “Fool in the Rain” by Led Zeppelin has both a twist ending and a musical gimmick (spanish flavored interlude) but a lack of a third item just makes it unique, not a novelty.
Also, videos do not count. It is hard when you have a video like “Thriller” which is virtually inseparable from the song but we must draw the line somewhere.

If a song is explicitly designed as part of a comedy act, it’s a novelty song (even if it’s a really good song, like Flight of the Conchords’ material).

I also don’t think novelty/non-novelty is a binary relationship. I think there are rock songs that have some novelty aspects about them (like Thriller, or things like Far Away Eyes by the Rolling Stones).

A song that’s funny isn’t necessarily a novelty song.

btw: Since I know you had a bit of an opinion about the novelty songs thing, I have been thinking about my own dubious definition of novelty song vs. regular song. My new thinking is along the lines of “If a song is about a specific character and a specific story, then it is closer to a novelty song. If a song is about a more universal “character”, where the listener applies the lyrics and sentiments to his/her own life, then it’s closer to a regular song.” I have to work on this a little more though, before I’m ready to argue about it “on the air”.