For Ireland (building off your emendation), we do not know anything about any of these stories before Christianization. Not for certain, at least. Though, before I play the role of annoying scholar coming in and stamping all over everyone's fun,I will note that there is some detail we might be able to tease out of the sources, but it is technically all speculative.

Some important details to keep in mind with Ireland as I get into this, by the time of our first historical records out of Ireland in the 5^(th) century, there are already Christians in Ireland. We know this because Saint Patrick mentions it in passing in his Confessio (here if you are interested). Our first extant pieces of literature appear in the 7^(th) century (and those are really early and probably from the very end of the 7^(th)), while the vast majority is from the 12^(th) century.

Regarding the Book of Invasions, it is highly unlikely this material existed at all pre-Christianization. The Book of Invasions is a thoroughly medieval Christian work that is inspired heavily by the Historia Brittonum, the 'Six Ages of the World' theory, and contemporary Irish politics. (For instance, have you ever noticed that the Fomorians are like... super weirdly really similar to the Norse? Yeah that's because they're just Norse analogues for political commentary. I'll get back to this in more detail in a few paragraphs.) The Book of Invasions is pretty heavily a text influenced by post 9^(th) century Irish political developments, and while there is a lost earlier version, the basic structure of the story is so thoroughly Christian (and the text a product of post-Christianization Ireland) that it can't be considered suggestive of pre-Christian belief.

Now! Did the various characters who appear in these early stories exist before? Maybe! But, not all of them. For instance, Mark Williams in Ireland's Immortals talks about how Midir and Boanann (two relatively obscure figures) appear to be actual pre-Christian figures based on locuses of place-names. Elsewhere, we know Donn survives into the 18^(th) century as a figure receiving actual veneration and minor sacrifices in rural Ireland, so, he's probably an old figure. Did they exist as Túatha Dé Danann? Nope. Why? Because Túatha Dé Danann is a later name! (Very exciting, I know). In the earliest Irish material these characters are called Túatha Dé (God-Like-Peoples [ish]), with the name Túatha Dé Danann (Peoples of the Goddess Danu) developing in the Middle Irish period.

Our earliest reference to the Fomori, before their redevelopment as anti-Norse propaganda, they are 'Farmers of the fields beneath the earth', a far cry from their monstrous form as forces of subjugation from islands to the north of Ireland, huh? Only after the 9^(th) century when the Norse raids start do the Fomori become a 'thing' in opposition to the Túatha Dé Danann, and it appears that the beings we know as 'Fomori' were actually just part of the Túatha Dé initially, as the genealogies are so closely entwined. For instance, Bres, The Dagda, Nuadu, and Ogma are all half-brothers, the sons of Elatha. If Bres is 'evil' because of his father being a Fomori, than so should The Dagda, Nuadu, and Ogma.

And to add an even further element of doubt into all of this: we don't even know if these 'groups' exists in the pre-Christian period. While we often imagine these traditions as part of an 'Irish Pantheon' or 'Irish Mythology' or 'Irish Cosmology', it is very unlikely that there would have been a unified religious tradition. It is more likely that there were specific regions with specific stories, not an 'Irish Pantheon' but 'Irish Pantheons'. So, we really can't say with confidence that the pre-Christian Irish considered the Túatha Dé, Fomori, Fir Bolg to be distinct 'things', or if they even existed that early.

Now that I have been terrible and brought the bad news about this, let me give you some good news however. The idea of the Áos Síde and the Otherworld is probably a pre-Christian belief, though, we don't know exactly how pre-Christian. The very basic idea of 'there is another world beneath the ground that is supernatural and has people like-us-but-not there' is probably more-or-less on point.

Why do we suspect this? Two reasons. Firstly, in other early Celtic cultures, we see a heavy emphasis on 'down' as the direction of the supernatural. Sacrificial offerings tossed in bogs, tossed in rivers, tossed in ponds, for instance. (Bodies of water are an easy way to go 'down' if you think about it, far easier than digging a big hole) This ties in with what we see in the early Irish material, that the supernatural world is beneath the ground, beneath the hills.

Now, the second reason we suspect this you might have guessed by that reference to this being visible in the early Irish material. As noted by John Carey, the location of the Otherworld actually changes in medieval Ireland. Initially it is thoroughly underground, beneath the hills. But then it suddenly transitions to being islands out at sea, particularly to the west of Ireland. Why would this happen? Well, simple cosmologic geography! As these traditions are being woven into a broader Christian tradition, 'down' becomes a problem. 'Down' is already occupied by Hell, and the early Irish religious scribes were very certain that the Otherworld was not Hell. They can't just move Hell, so, the Otherworld needs to go somewhere else. Can't go Down, Up, or Here, those are all occupied. Over There (East) is just Alba, Mann, Wales, and Britain, not really a bad LSD trip like the Otherworld is. Over There (South) is Iberia, and Over There (North) is 'vaguely where the Norse are'. So, Over There (East) is where the Otherworld gets dropped.

If the Otherworld was a purely Christian development, they probably wouldn't have developed it with this rather glaring issue of cosmologic geography that hey had to hastily fix several centuries later. Since it also fits in nicely with what we see in the archeological record pre-Christian Celtic cultures elsewhere, it seems to be a 'safe-ish' bet.

So, in sum: We don't know anything about the belief about these various Spooks and Supernatural Beings of pre-Christian Ireland (if they even existed back then). But! We are fairly sure that there was a supernatural realm beneath the ground and it had people in it. What those people did or who they were, we don't really know beyond some hesitant guesses about some specific figures (Donn, Midir, Boanann, Nuadu, among others) who might have been around that early on.

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Sources: (Can you tell that John Carey really likes this topic?)

Williams, Mark. Ireland's Immortals (Princeton University Press, 2018)

Carey, John. 'The Location of the Otherworld in Irish Tradition' in The Otherworld Voyage in Early Irish Literature (Dublin, Four Courts Press: 2000), pp. 113-119. (Provided for free by Dr. Carey here)

Carey, John. 'The Name Tuatha Dé Danann' in Eigse 18/2 (1981), pp. 291-294.

Carey, John. 'Nodons in Britain and Ireland' in Zeitschrift für celtische Philologie 40 (1984), pp. 1-22.

Carey, John. 'The Development of the Cesair Legend' in Éigse 22 (1987), pp. 37-48.

Carey, John. 'Myth and Mythography of Cath Maige Tuired' in Studia Celtica 24-25 (1989-1990), pp. 53-69.

Bruce, Lincoln. 'The Lord of the Dead' in History of Religions vol. 20 no. 3 (1981), pp. 224-241.

Müller-Lisowski, Käte. 'Contributions to a Study in Irish Folklore: Traditions About Donn' in Béaloideas, vol. 18 no. 1/2 (1948), pp. 142–199.

Sorry to be late to the game. I stumbled into this question - your tag failed to summon me. I suspect trolls were at work.

At this point, we have an excellent answer addressing Ireland, so that liberates us to move elsewhere. I hope you find something of interest in my humble volume. As you can see it is a homage to my dear old friend, Elisabeth Hartmann (1912-2005) who wrote her doctorial work on trolls under the direction of my mentor, Sven S. Liljeblad (1899-2000) and his mentor, Carl Wilhelm von Sydow (1878-1952). Sven gave me Hartmann's work to read in the 1970s because he regarded it as an excellent summary of troll beliefs and issues associated with them - including similarities in Britain and Ireland. Hartmann's work was published in 1936, which was extraordinarily bad timing. Although Hartmann had communist leanings, her father was a Nazi, so Hartmann's work found little play in Hitler's Germany (where Hartmann spent the war years under careful watch). Then after the war, Hartmann encountered further difficulties because of her father's affiliation with the Nazi's.

You probably have already read, but others may benefit from reading, about the complicated issues facing Hartmann in my brief essay, Nazis, Trolls, and the Grateful Dead: Turmoil among Sweden’s Folklorists. A few things seem clear when considering the limited early North Sea sources that address these supernatural creatures combined with early modern folklore collecting.

As has been observed elsewhere about Ireland, so, too, the Scandinavian, British, and Icelandic sources emerged with these types of supernatural beings seeming to be fully present. While sources are limited, it does seem that the sources are referring to entities that were believed to exist before conversion. In addition, because these similar entities across a broad swath of North Sea cultures seem to "zusammenhängen" (i.e. "hang together") as Hartmann described it (clearly borrowing inspiration from von Sydow and Liljeblad), there is at least some reason to see these many similar entities as having deep roots. It is not likely that the traditions diffused post-conversion. How one is to explain this folkloric curiosity is difficult, but whatever happened, it is easy to imagine it happening before conversion.

Throughout the region, there is a general consensus that these entities were/are extremely dangerous. While they were capable to having positive interactions with people, they could turn on a dime and the consequences of interaction too often turned out badly for those who crossed paths with the supernatural.

Because of this dangerous aspect, it was easy for early Christian clerics to cast these supernatural beings into the same pot with demons, declaring them as evil. In general and throughout the region, the folk resisted this effort, which is a hint at what might have existed before conversion: throughout the region, these supernatural beings continued to be declared as extremely dangerous, capricious, etc., but they were also firmly placed in a camp that was unaffiliated with the devil. Many North Sea cultures even maintained that there was a chance for Salvation for these entities, underscoring the neutral stance of the trolls (and their kindred by many names): when it came to Judgment Day, these supernatural beings, though unaffiliated with Heaven or Hell, had a final chance to be aligned with the forces of good.

Sadly, these are only hints at what existed in the prehistoric, pre-conversion world of Northern European cultures. Christian clerics subscripted to a worldview featuring a strict dichotomy of good versus evil. The fact that the trolls and their kindred were able to resist being placed in the evil half - despite the extreme danger that they represented - is the strongest hint of what might have gone before.

What sorts of stories were associated with these supernatural beings before conversion? That's of course impossible to say. The migratory legends that folklorists collected throughout the region are similar and they are often echoed in historic sources, but there is usually no good evidence that they existed before conversion (although they may have).

Whatever the stories were like, we can expect that they included humanity's fear of the danger involved and that the stories described the fixation these supernatural beings consistently have for interacting with people. These motifs are so ubiquitous that it is difficult to imagine the pre-conversion oral traditions without them.

If I might append to my own question, was there an understanding in Ireland of the previous settlers as documented in the Book of Invasions? My understanding is that was a history compounded to sort of bring the history of Ireland into alignment with a Christian tradition. Before Christianization, did the Irish have stories about the Firbolg, Tuatha, etc?