[The Might]

Interesting thread! I have taken the liberty to copy/paste part of a nice study on the origins and the history of the Ents posted by Andreas Moehn here http://lalaith.vpsurf.de/Tolkien/Fr_ents.html
The abbreviations used below are also explained at the bottom of the linked page.

The Eldest and the Firstborn

The statements about origin and age of the Ents are mysterious. Of course, no one would doubt that the Elves are indeed Iluvatar‘s "Firstborn", and they would have to be so to "cure" the Ents from dumbness. But why then are the Ents notoriously called "the most ancient people surviving in the Third Age" (LP) and "oldest of living creatures" (L131)? This can only interpreted that way that there were Ents before there were talking Ents. The first specimen probably were but mute and "dumb" or yet "unawakened" beings, looking and behaving just like another kind of tree. But of course, they were not ordinary trees. It cannot be doubted that Elves cannot just pass along and teach a tree at the wayside to talk and move, not to mention turning a forest into another Free People! There must have been an inherent potential of rational thought to the proto-Ents which only Iluvatar could have given to them and which was but waiting for the outside impulse to get active. Lothlórien recorded a unique hypothesis of their origin: "Some (Galadriel) were [of the] opinion that when Yavanna discovered the mercy of Eru to Aulë in the matter of the Dwarves, she besought Eru (through Manwë) asking him to give life to things made of living things not stone, and that the Ents were either souls sent to inhabit trees, or else that slowly took the likeness of trees owing to their inborn love of trees. ... The males were devoted to Oromë, but the Wives to Yavanna." (L248) If this was true, it would set real Ents far apart from "talking beasts", animate but soulless. No doubt, those spirits were sent before the Elves awoke but had to lie dormant till their proper time, so not to turn down the intended order in which the Children of Iluvatar would appear. This had not been allowed even to Aule’s Dwarves!


Are Ents Maiar?

Based of this statement it was often suggested that Ents were in fact Maiar. But there is much which speaks against. First, there is the usage of words. "Soul" in the sources is usually a crude translation of Elvish fëa, a kind of spirit very much distinct from a maia (MR). Maiar are very much above: Would it have been possible for even the greatest Child of Iluvatar to cure but one Maia from dumbness? The Wise of Middle-earth indeed believed or hoped that the "Ents and their wives being rational creatures would find some 'earthly paradise' until the end of this world: beyond which the wisdom neither of Elves nor Ents could see. Though maybe they shared the hope of Aragorn that they were 'not bound for ever to the circles of the world and beyond them is more than memory.'" (L338) Galadriel seemed to have known or sensed even more: Her farewell to Treebeard "until the lands that lie under the wave are lifted up again. Then in the willow-meads of Tasarinan we may meet in the Spring" (RK) indicates her belief or conviction that Ents - like Elves and Men (and Dwarves) - might possess an immortal component. However, a Child of Iluvatar derobed from his fána or body becomes a free fëa, but certainly not an Ainu! Second. The entish language is a further indication against them being Maiar. Real Maiar probably would not have bothered about developing any since they already possessed one: Valarin or a descendant thereof. Yet "the language they had made was unlike all others" (LP), even Elves had a hard time to learn "their tree-talk" if at all. The few examples of Entish recorded from hearing indeed do not resemble any other spoken in Middle-earth, least of all Valarin. Third: After the initial impulse of awakening was given to the Ents, they were capable of (consciously or unconsciously) awakening more trees. "Most of the trees [in Fangorn] are just trees, of course; but many are half awake. Some are quite wide awake, and a few are, well, ah, well, getting entish. That is going on all the time." (TT) Treebeard also remarks that "some of my trees are limb-lithe, and many can talk to me" (TT). Among those he had known "some good old willows down the Entwash". When he approaches Wellinghall, Merry and Pippin witness two unidentified trees capable of motion: they "lifted up their branches, and all their leaves quivered and rustled." However, those secondarily awakened trees were classified as Huorns, not as new Ents. Evidently, many trees, though not any tree, had the potential to do so: trees that seemed to be half awake or "quite wide" are also to be met in the Old Forest, notably Old Man Willow, (FR) and in Mirkwood (H). Without Entings they still were doomed to extinction – and with them the Huorns, for apparently no other species had any more the power to awaken them. By the late Third Age even the youngest Ent was already over 3000 years old. The surprising notion that the awakening of trees was not a one-time event but a permanent process is the strongest argument against the "Elves are Maiar" hypothesis. If all awakened trees harboured a Maia within that would have required a constant influx of Ainur from Valinor or outside of Aman to Middle-earth – many of which never again were awakened! An unlikely proposal. It may be assumed that Huorns rather resembled the talking beasts and thus were distinct from Ents by lacking the soul or fëa. But what should we make then out of the "spirit" (FR) that inhabited Old Man Willow?

In my opinion Andreas does a very good job at gathering the important data on Ents from Tolkien's writings and I agree with his own conclusion. The most likely explanation seems to be that upon hearing of Aule's dwarves Yavanna bargained "souls for the olvar" from Illuvatar. They seem to be lesser in "power" than those of the Maiar but are capable of reason and free will, their origins are of course another interesting topic.