[Morthoron]

People tend to overthink Bombadil's existence. As I've said often enough, take Tolkien at his word that Tom is an enigma from the story's point of view. However, outside of the plot Tolkien literally told everyone what Tom was, a personification of the "Oxfordshire countryside" he loved so well as a youth, and Tolkien considered Tom's inclusion very important personally, and not necessarily because he matched any cosmological or canonical conventions of Middle-earth.

Mythologically speaking, Tom (or Goldberry, for that matter) are not Middle-earth deities, but they share motifs culled from nature spirits common in British folklore and Greek mythos. Tolkien plopped them -- some would say indecorously -- into Middle-earth, yet still set them apart, strangers in a strange land, in their self-contained and bordered private playground.

The wise, including Gandalf and Elrond, have no idea what or who Tom really is because he is in fact alien in both historical and story convention perspectives. He is the first and older than all things because he predates Lord of the Rings from a publication standpoint, and his attire is due to his alter ego, a Dutch doll who once inhabited his children's nursery. The One Ring has no effect on him because he is an enigma from without the story inserted on a whim by the author.

Tom is Tolkien's private jest, and cannot be categorized as any sort of deity -- be it a Maia or Eru himself -- in context with Middle-earth.