"There are some things which, perhaps, should not be subjected to the systematic prying of man, whose beauty is not from any theological niceties but rather intertwined with the mystery of it. At the same time my mind is of such an inquisitive nature that some explanation- though likely inadequate by far- should be sought.
What then is the nature of faerie? It is the same nature as that of the hills and the forests and the soil.. When our fathers perceived the nymphs of the waters and the dryads of the woods it was because of their intimacy with the land. Faerie is far too earthly to be angelic. King James VI & I, in his Daemonologie, took the position that it was demonic, but a Calvinist of his calibre cannot be expected to be as tolerant of faerie as his Catholic predecessors certainly were.
Something else entirely then? The evidence- both folkloric and scholarly- to support the existence of all manner of phantasms and spectres is truly immense. Like the folk of faerie these are beings far too bound to this world to be angelic. Many are no doubt demonic; others may be the souls of men- purgatorians (though visitations from the damned are by no means unheard of), although one could debate whether they roam beyond purgatory or if their place of purgation is somehow upon this earth; but there are others still which can only fall into a third category, beings 'neither of the Heavenly Host nor of the Infernal Horde', as you say. A number of Renaissance Neoplatonists believed in discarnate intelligences which were neither angels nor demons, and connected somehow with the celestial bodies. Blessed Anne-Katherine Emmerich spoke of such 'planetary spirits, who are entirely different from devils, but who may yet have to be judged'. Of the Fathers of the Church I do not know. In regards to faerie itself, Fra' Sinistrari posits the existence of rational creatures possessing body and spirit, but distinct from man- scripture attests to the existence of such a race once, the antediluvian giants, offspring of incubi. 
A more earthy creature is described by St. Jerome in an event from his life of St. Anthony of Egypt, where the holy hermit comes across a faun and, confused as we might be, assumes the thing to be demonic and douses it with holy water, to which the faun responds by positively, clearly indicating that it is something else entirely. 
As I said in my last message, I am sure our fathers did indeed 'see' faerie. But did our ancestors behold these creatures in the same way as one man may behold another? They may have spirit and body, as Sinistrari suggests, but is their flesh like the flesh of man? Are they material in the same manner as we are material? Or do they partake of a matter more subtle than our own flesh? Like all living things they must possess souls- though these must not be immortal as our own, but mortal and utterly bound up with the earth. 
That is how I am inclined to answer anyway, a Tolkienesque perspective as you might say. Truly, the more I read Tolkien's mythologies the more I am certain that in them he has accurately represented an entirely Catholic- though distinctly Platonic- metaphysics and ontology. As the professor himself lamented, too many people try to read his legendarium with an allegorical eye, as they might Lewis, rather than as literature for the sake of literature. And yet in its themes and worldview it is the most Catholic of fiction literature. His letters and essays on other topics of course reveal a far more expressed relation to a Platonic and Catholic worldview. Tolkien presents a mode of thought that is indeed a very much needed breath of fresh air. I also see such thought as a call to return to our roots.
..." This letter was a response to a question about a line attributed by myself at the time to J.R.R. Tolkien in a letter to Arthur Greeves.
"[Family life must have been different] in the days when a family had fed on the produce of the same few miles of country for six generations, and that perhaps was why they saw nymphs in the fountains and dryads in the wood – they were not mistaken for there was in a sense real (not metaphorical) connections between them and the countryside. What had been earth and air and later corn, and later still bread, really was in them. We of course who live on a standardized international diet…are artificial beings and have no connection (save in sentiment) with any place on earth. We are synthetic men, uprooted. The strength of the hills is not ours."With more recent research into the origin of this quote I am able to correct my earlier mistake. This is actually from a letter by C.S. Lewis to Arthur Greeves in which he paraphrases Tolkien. The full quote is thus:
"Tolkien once remarked to me that the feeling about home must have been quite different in the days when a family had fed on the produce of the same few miles of country for six generations, and that perhaps this was why they saw nymphs in the fountains and dryads in the wood–they were not mistaken for there was in a sense a real (not metaphorical) connection between them and the countryside. What had been earth and air and later corn, and later still bread, really was in them. We of course who live on a standardised international diet (you may have had Canadian flour, English meat, Scotch oatmeal, African oranges, and Australian wine to day) are really artificial beings and have no connections (save in sentiment) with any place on earth. We are synthetic men, uprooted. The strength of the hills is not ours."The final sentence is a reference to the fourth verse of Psalm 95 in the King James Bible, "In his hand are the deepe places of the earth: the strength of the hilles is his also."
 This is a reference to Fra' Lodovico Sinistrari, a 17th century Franciscan priest and advisor to the Holy Office of the Roman Inquisition, and his work, De Daemonialitate.
 The story of the Faun is not from a life of St Anthony of Egypt, but rather from St Jerome's Vita Pauli monarchi, though the protagonist is still the same St Anthony. Nor is it a Faun that St Anthony first encounters but a "hippocentaur". St Jerome is uncharacteristically unsure whether, "the devil took this shape to terrify Anthony, or whether it be that the desert which is known to abound in monstrous animals engenders that kind of creature also, we cannot decide." Following this episode St Anthony finds the faunus, which speaks and gives some indication of its nature: "I am a mortal being and one of those inhabitants of the desert whom the Gentiles deluded by various forms of error worship under the names of Fauns, Satyrs, and Incubi. I am sent to represent my tribe. We pray you in our behalf to entreat the favour of your Lord and ours, who, we have learnt, came once to save the world, and ‘whose sound has gone forth into all the earth.' ".
 The existence of "subtle matter" was defined by the Second Council of Nicea in approving the following passage by John of Thessalonica:
"Respecting Angels, Archangels, and their powers, to which I also adjoin our own Souls, the Catholic Church is indeed of the opinion that they are intelligences, but not entirely bodiless and senseless, as you Gentiles aver; she on the contrary ascribes to them a subtle body, aerial or igneous, according to what is written: "He makes His angels spirits, and His ministers a burning fire." Although not corporeal in the same way as ourselves, made of the four elements, yet it is impossible to say that Angels, Demons, and Souls are incorporeal; for they have been seen many a time, wearing their own body, by those whose eyes the Lord has opened."