Frankly? There are weirder creatures in the Monster Manual. One of the guys in that picture looks like a minature owlbear, and there's nothing to rival illithids and certain other aberrants.
I favour cosmetics as a solution to your problems. Frex, take a zombie. Change its type to Aberration so it's no longer vulnerable to undead turning (but keep its hit dice) etc. Say 'This is a Shambling Mutant, it's got weird green skin and bulbous eyes'. Use the original stats. Presto, new monster which is not quite like anything else - it's slow, tough, and implacable. Or take a yuan-ti, call it a Sidewolf, and replace all the graphics of snakes with hideous mutant coyote parts dripping with venom. Presto, weird monster that can still constrict even though it doesn't have an apparent reason to do so, and that's freaky. Or take a troll, and describe it as the Cave Ghoul Dog, a four-legged reptilian creature with feathers and huge, pupil-less eyes, just because you can - there's nothing quite like that in physical shape, but physical shape has virtually no bearing on the rules.
Now, as to they why of the mutants... perhaps an asteroid lands. In the middle of a mass magical ritual. Being performed by aboleths. I think that's a good reason for horrible, slimy mutants to suddenly be everywhere - they've been contaminated by altered aboleth slime, which mutates people anyway.
