This is a really tall order. I don't think you can really get a fully logically consistent physics. The best you can do is a hand wave that sounds plausible enough that people don't think too deeply.
My best idea for the BRICK would be to go with the concept that is canonically superboy's power set, tactile telekinesis. They are not super-strong, but instead of a form of telekinesis that is limited. They must touch the object to exert their telekinesis, either because the field must expand out from their body to work or because they lack conscious control of the telekinesis and so their subconscious is using it tactile only.
This solves a huge number of problems that come up with super-strength. It explains why someone doesn't sink into the ground when they lift something hard, why the airplane's wings don't snap off when they try to lift the plan by it's wing, why the equal & opposite forces of throwing a gigantic rock at someone don't result in their being tossed backwards into a building etc etc.
A similar explanation can be used for their super-suitability. The same telekinetic field could be surrounding them. speedsters can't knock them over because they are using their telekinesis to hold themselves up!
The speedster could be explained with a similar approach, though it works a little less with him. Perhaps he propels himself with a similar sort of telekinesis ? It works better if instead of moving his legs super fast he simply hovers centimeters above the ground and pushes himself at high speeds. Of course this is more limited then the traditional speedster concept, he wouldn't be able to read or type at a computer at super speed for instance. Furthermore if he didn't have super-evolved reflexes he would still be quite vulnerable to anything that would force him to move quickly. His telekinesis may allow him to stop or turn fast when used, but he is still limited by his slow human-mind in recognizing threats and adjusting.
The speedster can survive hitting things with massive force because he doesn't hit them, his telekinesis does. perhaps that spreads the force from his one fist across his entire body, slowing him down rapidly but lowering the impact on any one point to a manageable level.
I think this approach works best if we explain the differences in telekinesis control coming down to the concept of "the human mind can't fully comprehend telekinesis " In theory it would be possible to fling spaceships by looking at them, but we haven't evolved to be able to do that and no one really knows how to make themselves do it. Instead we use our telekinesis to enhance things that come naturally to us anyways and subconsciously the telekinesis 'just works'
Of course, one still needs to explain where the telekinesis came from. Honestly I'm half tempted to suggest you don't try to explain any further. Saying "we figured out how to make telekinesis work" is one single hand-wave that you can get people to accept due to suspension of disbelief. Set consistent rules for how it works and just explain them. Trying to explain exactly how the telekinesis works further is likely to do more harm to suspension of disbelief then good, since once you bring up specifics people think about it harder and realize all the reasons it doesn't work.
However, if you do wish to try to go into more specifics, using modern physics, lets try something like this:
In the near future we have a revolutionary scientific breakthrough about how to control forces around us. We discover how to use a device to convert physical energy into potential energy and back again rapidly. It does this by projecting a special field of waves around the objects, and it can absorb or transfer energy across anything that passes through this field.
The really interesting thing here is to abide by thermodynamics and conservation of energy, which implies some cool limits to your superheroes. Imagine that your Tank goes in with a mostly full 'battery' of energy powering his field. When he lifts up a car and throws it he needs to transfer a significant amount of kinetic energy into the car to counteract gravity to lift it up. He can throw the car at someone by converting more of his potential energy into kinetic, the equal & opposite recoil doesn't occur because that kinetic energy is converted to potential. He will be using up lots of kinetic energy as he throws items around.
However, when the speedster runs up and hits him with supersonic force his field does the opposite, converting kinetic energy into potential energy. This recharges his 'battery' partially, giving him more energy to fuel his car throwing later. If he every uses up his 'battery' entirely he will be merely human.
As the speedster keeps being hit by punches from the tank he converts that energy into potential. However, his capacitor is limited as well, and eventually if he absorbs too much energy it can be over loaded and go boom. so no soaking up punches forever.
Of course entropy means that energy will have to be constantly lost with these exchanges. if they just trade punches back and forth both's batteries will slowly degrade as more and more of that energy dissipates due to entropy, maybe expanded across the entire electromagnetic spectrum to spread it out enough that it isn't harmful to anyone nearby (plus it's cool that a really strong punch actually causes a bit of a light flash that humans can see lol).
To further limit superheros from trading punches back and forth forever you could also imply that this device requires a unique fuel source, and they use it up as they trade energy. Thus the speedster isn't too worried that he is 'feeding' energy to the tank by hitting him, because he is still wasting the tanks 'fuel' by forcing him to have to convert between kinetic and potential energy.
Lets also put an upper bound on how fast one can convert between energy sources. If you get hit with a hard enough strike your field won't be able to covert the kinetic force into potential energy fast enough. Your going to feel the impact and be hurt by a powerful blow as some of the kinetic energy slips past your field and hits you. The more energy that your hit with the more that slips by, but it's not linear. If you get hit with X energy maybe 0.1x of it will slip through your field. if you get hit by 2x 0.15 slips through. 10x force lets 0.2 through etc; more force means more impact, but it's not where you can absorb exactly X without difficulty and anything over X will be fatal.
The other question is why we would use this to be superheros, when the technology has so many other applications. This is a real issue with almost any approach you use to justify superheroics. The best explination I have is that the power is limited to human minds and we use it the only way our minds know how to; theoretically it could be used other ways but we don't yet know how to harness it as such. For instance try out this scenario.
When they discover this amazing technology they also find a key weakness. Their best computer simulations are incapable of doing the calculations required to figure out how to exert this field accurately. Limitations on how we do calculations mean we are unable to generate a proper model quickly enough and thus we apply the energy translation field unevenly. This tends to result on very different forces being exerted across the body of an object, which ultimately lead to tearing it apart in a very unpleasant manner. It's unsafe to use computer controlled fields.
However, there are certain processes that human mind does much better then computers today (vision recognition, facial recognition, spacial orientation/awareness etc). In the near future we have not gotten any better at making computers do these sort of processes, thus the failed fails. However, in this near-future we have started to figure out the basis of computer to neural interface, connecting computers into our brains. Thus machines to control these fields are connected into the human mind. The human minds own unique processing ability is used to supplement the computers and do those calculations computers are still terrible at.
The problem is that the human minds are not human computers, we can't just plug into a human mind and tell it "figure this out for me". Instead we need to 'trick' the human mind into doing it's own process recognition and have the computers 'listen in' for the answer to the calculations it needs. This results in computers only being able to apply the field to those things that the human mind is already thinking about and processing correctly. Effectively TANKS are able to lift objects because when they are lifting the objects they already are calculating its position, shape, etc etc and the computer can use that processed information to power the field. In short the reason that we can't do even more with these fields is that we can only do what we can trick our minds into thinking we should be able to do...
Your speedster and tank are both using the same technology, but applying it in different ways. They would likely need extensive training to learn how to 'think right' to interface with the devices; and each was trained in using them in different manners. They both would likely receive similar protection from blunt force trauma because they have an awareness of their body and their minds can project an absorb the energy from that punch quick thought. However, bullets are so small and fast that the brain does not have time to process them, and so the computer can't use the field to absorb or redirect their kinetic energy.
