Is it possible to make a logically consistent set of laws that produces physics similar to that in superhero comics?

I'm not talking about stuff like radiation and mutations. I'm talking about mechanics (for now).

Necessary effects:

With superstrength, you can...

• lift objects weighing many tons without your feet sinking into the ground
• lift heavy objects at arm's length without overbalancing
• lift structures otherwise not capable of supporting their own weight

With superspeed, you can...

• land a supersonic punch without hurting your hand, yet still be vulnerable to bullets
• land a supersonic punch on a normal human without killing them
• run without worrying about the supersonic impacts of your feet making holes in the ground

A "tank/brick" character (strong and tough, not necessarily fast) has to be viable in a fight against a speedster. That is, the brick's fighting style relies on standing his ground. Without being particularly large or heavy, he must be harder to knock over with a high-speed impact than a normal person.

A brick can make high jumps from a standing start. A speedster can't.

The relation of speed to damaging ability is different than in reality. Even against normal humans, high-speed or sharp objects can still harm them, but low-speed impacts of massive objects are rather ineffective.

A giant doesn't have a problem with sinking into the ground.

Changing size changes your carrying capacity proportionately. A giant ant can lift many times its body weight; a human reduced to the size of an ant can't.

My initial thoughts / proposals:

The brick able to hold his ground suggests he has (passive or active) increased inertial mass. This in turn suggests that speedsters have decreased inertial mass. That is, it's not that they can generate more kinetic energy, but they can move faster for the same energy. Thus, their punches don't carry as much energy as a mundane object impacting at that speed. Because gravitational mass is unchanged, they can't jump as high as their speed would suggest. However, I don't think this explains why the Hulk is able to jump high.

Looking at it a different way, the underlying philosophy isn't "I have more money, so I can buy more." It's "I can buy things at lower prices." Properties of the world appear to matter only relative to your own capabilities. In essence, Superman can lift a car by its bumper not because he's exerting the tons of force needed to lift a car normally (which could tear the bumper off) but because, from his perspective, the car weighs less and he can lift it with less force. Likewise, it's not so much that the Flash moves really fast; it's that everything else is in slow motion from his perspective.

The square-cube stuff fits with this principle: doesn't matter if I get bigger or smaller, this patch of ground is still a flat surface made of the same material, it just looks like it covers a different area. I don't have a physical interpretation of this part, though.

The part about a speedster's punches and the part about mundane weapons might be consistent. It seems that the laws governing collisions are different in the super world. In an inelastic collision, kinetic energy is preferentially absorbed by the slower-moving object. Note this requires an absolute rest frame to be defined. This explains why a speedster isn't at serious risk from collisions with stationary objects. This greatly increases the damage-dealing advantage of high-speed low-mass objects over low-speed high-mass ones, creating broadly the correct effect in mundane combat. It explains the Juggernaut's unstoppable charge (or for that matter, the bus in Speed being able to ram cars with impunity - non-superhero action movies share a lot of these physics), and that bullets don't deform on impact.

This is just to show what I've considered already. Some may be redundant, some is insufficient, and I haven't fully reasoned out the other consequences of these. That's what I'm asking for help with.

Always assume a weak anthropic principle. Whatever laws this universe operates on, it must be able to have planets and recognizable life.

To clarify, given the direction the answers are taking:

The objective is not to justify super-powers in our universe. The idea is that even normal humans experience many things differently, since superhero physics appear to be a special case of action-adventure physics.

I recognized from the start that many super-powers make more sense as psionics. I neglected to mention that because I thought I made clear the approach I was taking. I want physical super-powers to be a consequence of, not an exception to, this world's standard physics.