So I've come to the conclusion that Adventure Time is the aftermath of a nuclear war. They talk about how there is no humans (except for finn) and if you look closely there is some desert areas filled with ruined buildings, cars, etc.
The human-like fish people living underground were probably decedents of survivors living underground in a fallout shelter. Years of living underground turned them into mutant fish people.
Susan Strong: The Hyoomen Tribe live in the ruins of an underground city. In the storyboard, a warning reading "Biohazard Danger" appears on the hatch, although this was cut from the episode. The inhabitants were possibly humans driven there during the war and later mutated.
*hyoomen sounds like human.
As for the candy people, Radiation turned candy into living creatures. Radiation is also the cause for magic (such as Jake's powers).
Also take a look at The Mushroom War.http://adventuretimewithfinnandjake.wikia.com/wiki/Mushroom_War
Opening shot of the theme song.
Ruins of a highway
The wizard battle area is an abandoned football stadium.
Marceline's memory, take note of the fucking tank and the ruins of a modern house.
An abandoned subway full of human skeletons!
Mutant fish people living underground known as the Hyoomen Tribe.
They call this "The Mushroom War" because the survivors described the nuclear explosion as a giant mushroom. (This is my guess)