Basic Trope: A creature that combines the scariness of a monster with the mysteriousness of a god and the ugliness of the blobfish (and sometimes with the vastness of the cosmos, the Nightmare Fuel of Room 101 and the incomprehensibilityof True Art).
Let's face it. It's really freaking hard to exaggerate an Eldritch Abomination, since it could be interpreted as already being an exaggeration of various alien and monster tropes.
Justified: In an infinite universe, it stands to reason that alien creatures might evolve in ways that would be outside of humanity's experience or understanding.
The observer is a stupid coward who had to go in for counselling after calculus and marine biology.
The Abomination comes from a universe with very different physical laws, and the mind struggles to comprehend it
Alternatively, Eldritch beauty with very benevolent behavior.
Or humans break the creatures' minds instead.
Alternatively: Uncanny Valley, where rather than being scary because it's weird and incomprehensible, something is scary because it's close to human, but not quite close enough.
Subverted: An alien makes humans think he's an eldritch abomination, but his motive is benevolent
Deconstructed: Instead of going mad from the revelation upon encountering the abomination and his mutated cultist slaves, scientists treat them as more of a discovery and a revolution than a monstrosity, thus the main conflict does not revolve around man versus abomination and his cultists, but between factions of the sane remainder of humanity that is divided between whether the abomination should be further explored For Science! or be altogether destroyed.
Due to the very nature of an Eldritch Abomination, the one that humans encounter in a story, although scary, is bored, alone, afraid and/or in pain, and desperately wants to be human, but it knows it can't, because its "job" is to maintain the universes' existence, often at the expense of those same humans.
While physically horrifying, the abomination isn't actually hostile or incapable of understanding humanity, nor are humans incapable of understanding it. However, its horrifying existence prevents there being any friendly relations with the majority of humanity, regardless of its intent.
The thing is so far beyond us in scale that it can't actually perceive or affect us anymore than we can a bacterium or virus. It's immune system can't adapt fast enough and we kill it just by going about our business in our new environment, an eldritch body. Alternatively, we're necessary to its digestive tract and have been living mutualistically for years without ever knowing it. They occasionally inject humans into members who lost a large amount due to illness or something.
The thing is fascinated with humanity, just like how some scientists are fascinated with insects.
Reconstructed: They're still not particularly friendly.
And just like humans (usually) don't deliberately jump on every bug they can see, the Eldritch Abomination causes only minor collateral damage.
The creatures develop medicine to better combat the disease that is people.
Through a mistake on their part, humans have ended up in a part of the universe where they really don't belong but are thriving, driving the native population near extinction. The eldritch creatures turn to their greatest minds in their bid to control this new population of introduced invaders.
Lampshaded: "They say that the well is haunted by an eldritch abomination. 'They' think anything that doesn't fit their preconceived notions of what a monster should look like is an eldritch abomination."
"'This being was what the mind conjures up when one hears the word "monster"; too many eyes, too many limbs, too many mouths, and dripping concentrated malevolence from every pore. All who met it's gaze died of horror, and their death was so utter as to became life again. What it couldn't control, it destroyed. What it couldn't destroy, it corrupted. What it couldn't corrupt, it sealed away.' yep, Eldritch Abomination alright."
Invoked: William the Villain tries to find, create or summon an eldritch abomination and watch what it does to humanity.
Exploited: As Invoked, but William is insane enough to grasp the true nature his summons and the way it wreak havoc upon human's mind.
Defied: "We come in peace!"
The creature strives to make itself understandable, going so much as reducing itself to existence in 3D space instead of 26D and taking the form of a cute little girl.
Discussed: "There are no words to describe the sight before me. Such things shouldn't exist. Will I ever sleep again? Will I be given the chance to try?"
Conversed: "Realistically, most aliens should be expected to be different from humans in both body and mind, and be rather hard to deal with. True monsters aren't all that out there."
Played For Drama: The monster has assimilated one or more people. If you kill it, they will also die.
The monster is completely unstoppable, but it's sealed. A huge part of the plot is trying to prevent the seal from breaking (works especially well if the seal is Powered by a Forsaken Child).
It's a sanity-raping abomination from the blackest reaches beyond space and time, ancient when the universe was young, the whole bit. No-one can get close enough to stop it before they go stark-raving bonkers.
