the Science of Superheroes

Superman and other paragons bend physics on such a scale, if any scientific explanation can exist it would be on a sub-particle level. He seems to control matter-energy and influence gravity.

 

They actually went on about that in Irredeemable with the Superman Expy the Plutonian, stolen from the wiki:

The Plutonian's powers are not physical but psionic, enabling him to subconsciously manipulate matter on an atomic level: allowing him to heat or freeze the air, see through objects, fly, render himself virtually indestructible, possess super strength and heightened senses, and make opponents more susceptible to damage. Modeus hypothesizes that if the Plutonian is made aware of his true abilities he would be able to alter probability, see through time and reverse entropy, concluding "and that's just if he moves from Kindergarten to grade school."

 

On another board, one of the members (I think that one has an account here as well) stated something from a Fantastic Four issue he read, "Reed Richards states Johnny Storm can fly cause things on fire have no weight" or something in that vein

 

Can't say what issue or universe, considering I don't read Fantastic Four

In one issue of Dennis O'Neil's run of Iron Man, Rhodey visited Hank Pym (I think to cure his headaches), Hank explained all the mass that comes and goes pass through a different dimension
That explaines the change in the size of the Hulk, too bad it doesn't explain the change in colors

I always liked the drawing of those gadgets of Marvel characters explaining their designs and how they work

 

Wasn't the latest thing for Superman that he psychically creates a shield around his body, and that this is also the field he uses to fly?

 

I respect the OP for starting with Superman, as he is probably the hardest pop culture superhero to explain. But I'll give it a go.

General superpowers - It's often described that a Kryptonian's powers are a product of Earth's yellow sun. That the red sun of Krypton either saps or just doesn't provide those powers like the solar radiation from a younger star. So I suppose that would mean that cell density was an adaptation that Kryptonians evolved to be able to function on a planet whose sun was dying. (For example, it's far colder on Krypton, gravity is stronger, etc.) We might even assume that humans could evolve in this direction if we are still around when our sun starts to die.
Durability - I've often heard (as the op said) that superman's cellular structure is more dense than that of a human. So we have to believe his skin cells are at least as dense as steel. Probably developed in this manner to avoid the more intense radiation of Krypton's red sun. Thicker, therefore bulletproof, fireproof, etc.
Strength - If his skin cells are more dense, then there's no reason its not the same story for his muscle cells. Allowing them the ability to generate greater force per square inch or however you want to describe it. And, much like Lance Armstrong, perhaps he feels substantially less muscle strain due to lactic acid buildup.
Speed - A combination of denser muscle tissue and brain cells, allowing for faster reaction speeds. I read somewhere he'd also need joints with less friction to avoid overheating and degrading and that comparatively lighter bones also would allow him to move more quickly.
Flight - The age old argument, is his flight not just an extension of his ability to leap tall buildings? Not sure about that, but seeing as how we've already established the gravity of Krypton was much stronger than Earth, leaping is easy to believe. Flying would be something of a matter of the energy stored in his cells being lighter than the atmosphere of Earth? No idea.
Super Vision - If the rest of Supes' cells are denser than that of a human, then lets assume the cells of his eyes are more dense as well. Probably quite complex as well. So it's not that he sees things via x-ray technology, but that he sees the world entirely differently. He can perceive substantially more of the electromagnetic spectrum than humans do (which is actually quite believable because certain animals can even do this). As far as heat vision goes, the process that allows him to perceive these various spectrums, could potentially result in energy expulsion (just like medical radiographs produce radiation). So anyway, he manipulates this anomaly and often weaponizes it.
Super Hearing Also a lot more believable as there are several animals on Earth with more cells and small bones in the ear that allow them to pickup sound at greater distances and different wavelengths than humans.
Super Breath - this i'm not so sure of... I mean, cooling something to the point of freezing temperatures is something I have no idea how a living body could do. Seems strange and if we were trying to make a realistic superman (i.e. Zach Snyder's Man of Steel) I'd say it should probably be retconned. Super breath on the other hand, is another feat of strength of the muscles in Superman's lungs.



Superman. A fascinating creature.

 

Now, with the suspension of belief that Superman is a possibility, the skill sets of many other heroes are soon to follow.

Wonder Woman and Thor for instance, assuming their cell structure is of a similar density (but not quite to the degree of Superman). But that doesn't really include their weaponry, their armor and their tech. So, you could take a look at those individually. Now a lot of them are explained by "enchantments," but if we are to believe the 2011 Thor film on Asgard, "science and magic are one in the same thing." Could be a similar case in Themyscira.



Batman is a hell of a lot easier to explain. Years of intense physical training (by masters in several martial arts) caused by an obsessive goal oriented mentality. Combine that with acute intellect and strategic mind, mental instability, virtually unlimited human resources and a lot of luck, and you've got a recipe for... well disaster, but it seems to work out for Bruce Wayne. Several of his villains aren't too hard to believe either. Joker, Riddler, Penguin, Catwoman, Bane... Maybe heavy on the theatrical side, but practically come straight outta real life. I think just looking at Nolan's Batman trilogy, and comics like Frank Miller's Year One, you can easily see how Batman is possible. And with a couple soft-retcons so are the majority of his rogues gallery. That's why everyone loves Batman!



Once you suspend the belief in Batman, it's easy to go down the list of human heroes too. Green Arrow, Hawkeye, Iron Man, War Machine and all his tech-based villains. With Iron Man, it's all about the power source. I think the bigger you make Iron Man's suit, the more imminent it's real life counterpart becomes. Another huge problem from my understanding, is "cabin" pressure at certain altitudes and velocities. But if he didn't fly super fast, he'd basically just be Batman... So we'll give Tony this one.