Which animal has the largest organs of all animals?

It depends on which organs you mean. In relation to body size, here are some species that have won that record.

eyes :

Small amphipod crustaceans of the Hyperiidae family. There is very little information about them, so I don’t know exactly how big their eyes are, but I do know that they are proportionally larger than any other animal.

Stomach :

The black gobbler, a type of deep-sea fish. With its huge distensible belly, it can eat fish up to 10 times its size! Despite this, sometimes its eyes are larger than its stomach (figuratively, of course), and it eats prey so large that it breaks open and dies.

Tail :

The Takydromus sexlineatus (long-tailed lizard), also known as the Asian grass lizard. Its tail is over three times as long as its body, and it has the ability to grow back after being torn off. It is also prehensile, functioning as a fifth limb for grasping branches.

Legs :

I deduced in a previous answer that this would have to be some kind of harvester. Better known as folcids, these arachnids are not actually poisonous, contrary to popular belief.

head :

I’m not entirely sure, but the erythrischids, an obscure family of Triassic reptiles, would be up there. Their huge heads were most exaggerated in the genus Erythrosuchus, whose skull comprised more than a fifth of their body length, at more than a meter long.

Mouth :

At least relative to body size, I think the winner would be the pelican fish, another deep-sea rarity. Its mouth is much larger than its body, and – like the black gobbler’s stomach – it is used to gobble up larger fish.

Peak :

The famous hummingbird of South America. Its impressive beak is longer than its entire body (something that cannot be said for any other species of bird) and is used to draw nectar from deep flowers inaccessible to other nectarivores.

wings :

Among the existing species, it is the traveling albatross, but the extinct Pelagornis sandersi beats it, with a wingspan of 7.4 meters. The seabird family to which it belonged, Pelagornithidae, is known for its large size and serrated “toothy” beaks.

language :

Unsurprisingly, chameleons have this title, as their tongues are twice as long as their bodies. They shoot this out of their mouth with incredible speed (although not as fast as another creature ) to catch unsuspecting insects with a sticky pad.

Brain :

This title does not belong to humans (although we have the highest encephalization quotient, something different), but to shrews, whose brains make up 10% of their body mass. However, their neural tissue is much less dense than ours.

Skin :

There’s no official word on which animal has the highest skin-to-body-mass ratio, but I’d bet on the African elephant, because of all its wrinkles and folds (plus its huge, but spindly, ears). Giant animals produce a lot of heat, so they need a lot of surface area.

Liver :

It would definitely be some kind of fish that doesn’t have a swim bladder, maybe a shark. Basking sharks, for example, have livers as big as cars that make up a quarter of their mass. The liver is full of dense oils that are used to control its buoyancy.

Egg :

I guess an egg is more of a cell than an organ, but it doesn’t really matter. In any case, it’s the New Zealand kiwi – despite being the size of a chicken, this strange bird’s egg is 10 times the size of a chicken egg, as vulnerable chicks need to be well-developed at hatch.