The Maiar

In J. R. R. Tolkien's fantasy stories, the Ainur are a race of spirits. The Ainur ["Holy Ones", in the ancient Elvish language of Quenya] were the first of the creations of Eru Ilúvatar ['The One Father of All'] out of his thought, who aided in the creation of the world. The few most powerful and greatest of the Ainu are called the "Valar" [powers], the uncountable numbers of others are the "Maiar" [beautiful ones].

in the Timeless Realm, before the world was made, each of the Ainu was taught the art of music. Together, they made the Ainulindalë [Song of the Ainu], called "the Great Music": the story of all creation sung long before the material world was made. Further, each of the Ainu is associated with some element of the world and the Vala that personifies it.

Ainu are shape-shifters. They normally have three forms: one invisible, one like a noble and beautiful elf (because they admire the elves and wish to make them comfortable) and at least one more native form that expresses their purpose in the world. Further shape-shifting is recorded, but not common. While in the world, Ainu are ageless, but can suffer injury and even destruction, when they must revert to bodiless invisible forms.

The Ainu are featured in much of JRR Tolken's "The Silmarillion". The most complete Tolkien description and naming of the countless Maiar is in "The Book of Lost Tales", quoted here as they are leaving the Timeless Realm to create the material world after the Great Music. Translations from Quenya are in [brackets].

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[AIR]
Behold, Manwe Súlimo [(good-man) king wind] and Varda [queen] the Beautiful arose. Varda it was who at the playing of the Music had thought much of light that was white and silver and of stars. Those twain gathered now wings of power to themselves and fared swiftly though the three airs…

With them came many of those lesser Vali [powers (also "Valar")] who loved them and had played nigh them and attuned their music to theirs, and these are the Mánir [(good) spirits of the air] and the Súruli [spirits of wind] the sylphs of the airs and of the winds.

[FIRE]

…Now swiftly as they fared, Melko [flame] was there before them, having rushed headlong flaming through the airs in the impetuosity of his speed, and there was a tumult of the sea where he had dived and the mountains above him spouted flames and the earth gaped and rocked; but Manwë beholding this was wroth.

[WATER]

Thereafter came Ulmo and Aulë, and with Ulmo [fluid] were none, save Salmar [harpist] only who was after known as Noldorin [wisdom], for good though the heart of [Ulmo,] that mighty one he thought ever deep thoughts alone, and was silent and aloof and haughty even to the Ainur;

[EARTH]

with Aulë [invention] was that great lady Palúrien [earth-mother] whose delights were richness and fruits of the earth, for which reason has she long been called Yavanna [fruitful] among the Eldar [elves].

About them fared a great host who are the sprites of trees and woods, of dale and forest and mountain-side, or those that sing amid the grass at morning and chant among the standing corn at eve. These are the Nermir [fays of the meads] and the Tavari [fays of the woods], Nandini [fays of the valleys] and Orossi [fays of the mountains], brownies, fays, pixies, leprawns [leprechauns(?)], and what else are they not called, for their number is very great: yet must they not be confused with the Eldar [elves], for they were born before the world and are older than its oldest, and are not of it, but laugh at it much, for had they not somewhat to do with its making, so that it is for the most part a play for them; but the Eldar are of the world and love it with a great and burning love, and are wistful in all their happiness for that reason

[WATER]

Now behind these great chieftains came Falman-Ossë [Surf Maker - Sea Lord]of the waves of the sea and Ónen [Sea Lady] his consort, and with them the troops of the Oarni [sea-dwellers] and Falmaríni [surf-dwellers] and the long-tressed Winglidi [foam-nymphs], and those are the spirits of the foam and the surf of ocean. Now Ossë was a vassal and subordinate to Ulmo, and was so for fear and reverence and not for love.

[SPIRIT]

Behind him came Tulkas Polórëa, [steady might] rejoicing in his strength, and those breathren the Fanturi [spirit masters] Lórien Olofántur, [the Slumber Dream-master] and Vefántur Mandos, [the Doom-master of the Dead], … and the twain who are known as the Tári [Queens] Fui Nienna, [the Weeping Mistress of Death] and Vána Tuivána, [the Ever-Young Mistress of Life]…

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Thus the fae, mer and furry fit in Tolkien's world as these Ainu when in visible form.
Enjoy your play!
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ref:

The Book of Lost Tales - One (posthumous) JRR Tolkien, Ed CR Tolkien
copyright (C) 1983, the Estate of JRR Tolkien

The Silmarillion, JRR Tolkien, Ed CR Tolkien
Copyright (c) 1977 by George allen & Unwin Publishers) Ltd,

copyright material quoted under "fair use" rules