the lord of the rings - Who or what is the oldest sentient being in Tolkien's lore?

The Hobbit, The Lord of the Rings, The Silmarillion, The Histories of Middle Earth, all lore related to this universe is acceptable fodder. Regardless of their power, susceptibility to The One Ring, amount of appearances, or any other constraint, who or what is the oldest?

Since Eru is the "easy" answer, then who or what is second? Any canon source, including letters, is acceptable.

I am asking this as more defined version of this recent question which was put on hold.

And if it matters, the criteria would be oldest at the end of LotR or whatever place he left off in his tales whether the being was alive or not at that point. Example: if being 1 was 999 years old at point A and died, and being 2 was 998 at point B (years after point A) and died, being 1 was oldest in the lore.

(I am not well-read in the Histories and letters and such. If he continued the tale much past the end of LotR, then that is the cut-off point. Oldest sentient being, alive or dead, at the end of canon.)

If you have a question about if some source counts, ask yourself: Did it come from JRR or Christopher working from his father's notes? If the answer is Yes, then it counts. If it does not come from the family, then no. I can trust scholars, but would like the trail to be only one degree of separation. If your case is compelling enough, a pass may be granted.

EDIT

If it's not bad form, can I extend the question to the oldest four? Eru is too obvious and as Kevin comments, "Eru was clearly first, he created the ainur second, and it's generally indicated that Tom Bombadil is tied to Middle-Earth and so third." The "generally indicated" thing is not decisive, but, if this is indeed accurate, I'm curious to know just a little bit more. Please either play along with me, or slap my hand for grabbing too many cookies. It's a fascinating and complicated history I know too little about. (I do plan to remedy this someday.)

NEWER EDIT

I just noticed this question still gets viewed and was active a few months ago. Let me further clarify. I am after the oldest entity AT ANY POINT in the canon. If a creature lived to be 99 years (I'm using low numbers to keep it simple) and then died, and another lived to be 98 at the close of the canon, the dead one wins. Living, dead, doesn't matter. Age at end of canon is all that counts.

Answer

Eru created the Ainur and they sang the world into existence, presumably including Tom Bombadil so yes, the Ainur would be the eldest after Eru. Since Bombadil is in essence an Earth elemental and tightly tied to Middle Earth, he could only be as old as the world itself and so younger than the Ainur (and the Maia like Gandalf).

Another contender would be Ungoliant whose origins are unclear. The Silmarillion states (emphasis mine):

The Eldar knew not whence she came, but some have said that in ages long before she descended from the darkness that lies about Arda, when Melkor first looked down in envy upon the Kingdom of Manwë, and that in the beginning she was one of those that he corrupted to his service.

This suggests that she was somehow from outside the world and perhaps even independent of the Ainur's song (or even Eru himself?). I read the Lost Tales years ago and don't remember but according to this:

In The Book of Lost Tales, Ungoliant's history is even more mysterious then what is implied in the published edition of The Silmarillion. Here, even the Valar did not know of her origins, and she was portrayed as a primeval spirit of night, and believed to be a creature bred of the darkness of the Void.

This suggests that she is indeed independent of the Ainur (the Valar) and might be older then they. Finally, I found this page that states:

"Within this structure there are as almost always a great many points of difference between the first story and the later versions." "In the tale her origin is unknown, and though this element may be said to remain in The Silmarillion ('The Eldar knew not whence she came', ibid.), by the device of 'Some have said....'a clear explanation is in fact given: she was a being from 'before the world', perverted by Melkor, who had been her lord, though she denied him. "

and

"Mayhap she was bred of mists and darkness on the confines of the Shadowy Seas, in that utter dark that came between the overthrow of the Lamps and the kindling of the Trees, but more like she has always been; ...."

So, at the very least she seems to be as old as the Ainur but may be older still.