One of those old games that was pretty weird that sticks out in my mind was the first Teenage Mutant Ninja Turtles NES game.
While it did have Foot Soldiers, Mousers, Bebop and Rocksteady, something resembling Metalhead (though it isn't actually), the Technodrome, and Shredder as enemies, as well as beings that could be interpreted as Rock Soldiers*, it also had various giant bugs, boomerang-throwing jumping guys, vaguely ED-209-like robots, chainsaw-wielding guys, frog-men, bomb-dropping mini-balloons (with the Foot symbol on them), killer seaweed, jetpack soldiers, and a few other things I'm sure I've forgotten (they're odd, but even though these particular things clearly aren't based on any particular things in TMNT, they're not especially weird by the standards of the setting), and then also had guys on fire** who shoot fireballs that turn into what I've never been able to see as anything but hopping legs made of fire, odd pink pillbug men, flying jellyfish, running and jumping quill-firing porcupine things, armless robot kangaroos, firebreathing robots with heads that detach and fly around when you kill them, eyeballs with legs, dudes who split into up to four smaller dudes when you hit them***, and a few other really weird things.
And making things weirder is that in some environments, the groups of enemies in an area will randomly change while you're still in it during moments where there's no enemies "on camera," meaning you can go from fighting firebreathing robots, bomb balloons, and giant fleas to fighting guys on fire, dive-bombing miniplane things, and eyeballs with legs.
Making something that's still pretty weird by the standards of the franchise that came up with the weirdest place/set of places to be called Dimension X is an achievement.
*There are beings who shoot some sort of crescent-shaped projectile and spend most of their time in an invulnerable curled up form. This doesn't actually resemble the Rock Soldiers very strongly, but I've seen other people interpret them that way, and it's a logical enough comparison to make.
**They're actually described as being "ex-pyromaniacs" who have managed to somehow survive setting themselves on fire. Ex-pyromaniacs?
***They're among the weirdest and toughest enemies in the game, incidentally, because it takes one hit to split them in two, then you have to hit each half to split them again, and each smaller variation is faster and better at jumping, plus, if I recall correctly, each small guy normally takes about four hits to kill. Plus they're so fast and good at jumping that they actually don't jump right (the engine doesn't seem very good at handling enemy jumping), and sometimes just kind of float around erratically. Since it takes about nineteen hits to kill these guys and they divide into such fast, erratic enemies, it's really good to have the cannon secondary weapon, which wipes out most enemies in one hit, and bypasses the death spawning actions of enemies such as that one. Plus the cannon also has a huge area it covers, so smaller/erratic enemies have a hard time dodging it. Plus, once you reach the third stage, you have the opportunity to gather well upwards of sixty shots of cannon fire thanks to some quirks of the level design. The lesson is that you should always go for the cannon.
Incidentally, the dividing guys also look rather like they're naked.