So I'm sitting around watching my current anime of choice (One Piece), and several characters make that face we've all seen where their jaw drops until their mouth is bigger than their head and their eyes somehow stretch two or three inches out of their sockets. Normally I would simply dismiss this as an animation effect to emphasize their shock, but then I say to myself, "it's One Piece, anything's possible. Maybe they really are making their faces stretch like that."
That got me to wondering, how would they be able to do that? Then I started thinking and realized that there were a lot of things that are portrayed as humanly doable which, I'm sorry, just simply are not. A prime example is Rokushiki, a form of martial arts which allows its users to move at invisible speeds, and while it is possible to strike in a way that reduces your opponent's ability to register your strike, the sheer speed exhibited by several characters in the show is just impossible in this reality.
So I began to think about what made it impossible. Answer: Physics, especially gravity. The human, and as far as I know biological beings in general, cannot generate enough power per unit of weight to move that fast. When gravity is significantly reduced however, it is much easier because your weight is reduced. The more your weight is reduced, the more your push off from the surface is increased.
That of course though is not enough. There are other things that slow a person down, friction, air resistance and many others. So I began to think, and then I realized what it was. The forces of physics are drastically weaker in universes such as One Piece. This allows seemingly superhuman feats because the things holding people together are much more fluid and flexible than in our universe, where things are rather set and consistent.
It is also possible that a degree of this flexibility of reality is present in all universes which feature super-humans and impossible things. The more widespread impossible things are in a universe and the more impossible they are, the more flexible their reality is.
And in some universes, these flexibilities might only apply to certain things, living people for example. In flexible realities, the number one binding agent of physical form might not be the forces of physics as it is in our dimension, but rather the soul. In our dimension, if the forces holding your body together are disrupted, you disintegrate, bang you're dead. In a dimension where your soul holds your constituent particles together in a form, it is possible that mutative energies such as gamma radiation could alter your form without killing you because your form is not reliant upon the forces of physics. This would also lend credence to the existence of ghosts in such universes, and unsurprisingly in almost every universe I have encountered where such physical mutations are possible, there are ghosts, spontaneously created sentient beings and other such oddities.
So my answer to why do they have cool powers we don't: they exist in a more flexible reality.
Now what does this mean for dimension jumpers who might stumble into one of these universes?
Well, assuming you maintain the strength of the forces holding you together across dimensions, you will be considerably stronger and/or more durable than most people in a flexible dimension, because things in a flexible reality are held together by much weaker forces. Thus to them, you might have the density of metal or stone rather than flesh. You would also probably be considerably stronger due to weaker gravitational forces, who knows? You might have super strength just because you're from our dimension! Or if its a very similar reality, then you might just have a resistance to mutative and transformative energies.
But if your bindings change in proportion (soul vs physics) to match whatever universe you happen to visit, then you could very likely acquire metahuman abilities through whatever methods are available in that universe, and possibly even carry them with you to other dimensions! Wouldn't that be cool?
Please note that this is all conjecture and CS is not responsible for any accidents befalling dimension jumpers who try to get superpowers from gamma radiation in Marvel universe.