Demons from the Ancient World

Tolkien allows plenty of room for creatures of unexplained origins to exist in his stories without requiring us to assume that they have unique origins. Tom Bombadil, Ungoliant, dragons, giants, etc. all have possible--even probable--natures among those outlined by Tolkien, although he does not explicitly tell us to which order each belongs.

Creatures vaguely referred to as "giants" appear only in "The Hobbit," as far as I know, and even there in a possibly superstitious sentence. I believe it's likely that by the time "The Lord of the Rings" was in publication there were no more of these presumably manlike giants.

The point in time at which Ungoliant comes into the story and her latent potential for extraordinary power (having feasted on light--itself an indication that she was no mere incarnate creature--she became more than Melkor could master) suggest that she was one of those primeval spirits that became Ainur. Yet she may not have been an "official member" of that order since it seems that her presence in Arda was unsanctioned by Eru. This fact might qualify her for anomaly status, though I do believe that her true nature is not enigmatic.

Tom's a bit more of a puzzle, and although we may not need to look outside the mythos for the truth of him, I believe he is the one singularity for which this approach might be acceptable. It becomes silly, however, to attempt to quantify his power level in relation to Arda "natives" when we entertain the idea that he may not even belong there.