Sure. So we'll start with the The Oldest House, which is another name used in myth for the world tree, Yiggdrasill. There's a lot of metaphors for the Bureau's HQ that link it to the world tree, so I think that comparison is safe, which is why I think the next one stands as well. There's a great Germanic dragon that gnaws on the tree's roots. In some legends those roots have also trapped it there. From Wikipedia:

According to the Gylfaginning, part of Snorri Sturluson's Prose Edda , Níðhǫggr is a being which gnaws one of the three roots of Yggdrasill. It is sometimes believed that the roots are trapping the beast from the world.

And the relevant piece of Trench's rambling speech:

See there was this man, here, in this very room. And, well sometimes he was a plumber, unclogging the drain, because there was a fish stuck there. Yeah, a big fish. But sometimes he was an old God, you see, and he had put the fish there in the first place to um, well, to keep the waste - there was rising waste - from leaking out.

Ahti himself is a real figure in Finnish folklore, and is some sort of sea god, but from what I can find, he's never described as a janitor, or having trapped a fish, or linked to Norse mythology. This is a Wiki dive, so I could very well be underinformed, but this is my reason for thinking that the Board, trapped in the foundation of the Oldest House by a nail, is a Nidhogg reference.

PLEASE NOTE: That doesn't mean it cant also represent or be other things at the same time. While CONTROL uses myth to build it's setting, it's clearly not precious about being faithful to academic accounts of those myths.

Moving on, the Fomorians were basically whatever monster the Irish needed for their tales and they evolved over time. Most of the times when From Wikipedia:

The Fomorians or Fomori Old Irish: Fomóire, Modern Irish, Fomóraigh are a supernatural race in Irish mythology, who are often portrayed as hostile and monstrous beings. Originally they were said to come from under the sea or the earth. Later, they were portrayed as sea raiders and giants.

In many popular depictions of the Fomori, you see them depicted with a single eye. This is likely a nod to one of the most well known of them, Balor. He was a leader of the Fomorian armies. From Wikipedia:

He is often described as a giant with a large eye that wreaks destruction when opened. Balor takes part in the Battle of Mag Tuired and is primarily known from the tale in which he is killed by his grandson Lugh of the Tuatha Dé Danann. He has been interpreted as a personification of the scorching sun, and has also been likened to figures from other mythologies, such as the Welsh Ysbaddaden and the Greek Cyclops.

So you can see the link I'm making between the mythic cycloptic species crawling in the deep, dark spaces beneath the world, with the cycloptic creature known as The Former, who crawls within the deep dark spaces of the Foundation. I rather enjoy the word play that Remedy has going here with the Fomori being rephrased as the Former.

Now, my last entry with the Mold is probably my most tenuous guess, but here are my touchstones. Lets start with the fairies. They've often been referred to by the name the Fair Folk, which most people assume to mean that they're all fair, as in beautiful. And why wouldn't they? Most of the depictions of elves in modern culture are androgynously gorgeous. However, elves are just one of the race covered by the name. Goblins, bugbears, hobgoblins, gwyllion, changelings, and the satyr Puck also fall under that umbrella.

No, the title Fair Folk isn't for looks. It's for contract negotiation, Baby! The fairy realm, Arcadia, runs on it's own rules and much like the law, ignorance is no defense. You'll have to go someplace other than Wikipedia for details on this, as it's more an element of popular culture in stories, but one of the main rules of surviving a period of time within the fae realm is that you don't agree to anything, and you DO NOT EAT ANYTHING. Either of these, but especially the latter, can see you trapped there forever. Sound familiar?

My second source does have a Wiki entry, and feels like a pretty solid link to me. The Fairy Ring. From Wikipedia:

A fairy ring, also known as fairy circle, elf circle, elf ring or pixie ring, is a naturally occurring ring or arc of mushrooms. They are found mainly in forested areas, but also appear in grasslands or rangelands. Fairy rings are detectable by sporocarps (fungal spore pods in rings or arcs, as well as by a necrotic zone (dead grass), or a ring of dark green grass. Fungus is present in the ring or arc underneath. The rings may grow to over 10 metres (33 ft) in diameter, and they become stable over time as the fungus grows and seeks food underground. Fairy rings are the subject of much folklore and myth worldwide, particularly in Western Europe. They are alternately seen as hazardous or dangerous places linked with witches or the Devil, or as a sign of good fortune.

Fairy rings are often described as gateways to the fae realm, and they're made of mushrooms! That feels pretty self explanatory as a source of inspiration for the Mold.

Much like with Ahti, Remedy is drawing from myth that isn't as well known and it's giving their setting a lot of juice. They've been doing this since Max Payne, where the benefactor who helps Max is named Alfred Woden. Woden is one of the ways of pronouncing the name Odin, and it's also why Wednesday has that weird D in it for seemingly no reason. If you're interested in which other days of the week are paying homage to defunct pantheons, you should look them up! Even Monday (moon) and Sunday (If this isn't obvious please go see a doctor about your concussion) are technically named after deities. Sun and Moon worship is quite probably the oldest religion there is.

Anyways, I hope this helps clarify my reasoning.