They definitely will need better shoes.
One 10t strength, with mass 100kg - will jump probably 100m high (or less because of air) with initial velocity ca 44 m/s, duration of jump 0.045sec, 4.5 sec fly up and 4.5 sec fly down times.
Height of jump is linear with force/strength, speed linear to sqrt(), so 5t man jumps 50m high, 31m/s velocity (44/sqrt(2)), 1t man 10m high, velocity ca 14m/s.
The calculation is a bit odd, I assumed they able to apply that force evenly along 1m acceleration path, and they limb working fast enough for that.
The nice thing, they can not worry about the strength of skyscrapers roofs, because they can fly Daedalus/Icarus style - less energy, more speed, safer, less skyscraper depended, more flexibility(no needs to sit on the tallest skyscraper and wait for action). Nowadays they may use kevlar instead feathers and wax, for they flying suits. Also how base jumpers shows(with their squirrel suits) it will be pretty fast, may be faster then skyscraper-jumping, and definitely more flexible in therms of trajectory.
That initial sped, 44m/s, for 10t man, is actually base speed for all his legs, arms movements. If assume 10kg each, 10t divide by 2(2 arms have 10t combined), apply sqrt(5) - it's ca 100m/s limit.
Not bad actually, definitely he can crash walls, etc like 20-pound ancient cannon, or trow something pretty massive(for that speed) with similar results.
Run speed is limited by the speed of leg movements - so 100m/s best max for 10t man, so no sonic booms whatsoever. Probably he will move faster by flying with some suit extensions. Using all his 4.5 limbs. His total power is 6000 horse power (10t force per 0.045sec for 2 limbs is 3000 horse power) - for aircraft with much less power and higher drag - makes 600km/h La-5. So theoretically speaking it's enough for 2Mach speeds. So subsonic speeds he will do, and it's 3 times faster than the maximum speed he can run with same assumptions. So I would suggest buy kevlar wings, and sell it to that 10t man, with 300% profits.
If he can't do that 6000 hp constantly for a long time - then yes jumping may be a good option, but still not much better then gliding, and wings will help to manage that jump trajectory like squirrels do.
One punch, with 10kg arm and 5t force, will have duration 0.02sec, so if you haven't ended your opponent in 1 second with 100 punches, probably your actions are useless and you should go and take .50 BMG - will solve your problem, if not, you sucks, he rocks.
Equilibrium(film) is actually nice representation of that style fights. Not exactly, but looks like they keep that in mind.
Force and buildings
10t is a lot if applied on a small surface. Ability to withstand 20t force per square meter that is pretty strong and usually overkill, from an industrial point of view, for common situations.
So roof workers will definitely ask, who should pay for that damage. Everything may be tested with old canon blasts, if it will stand then it will stand the man.
Actions in compartments
As typical duration, at max speed(100m/s) movements, are 0.02 and that is 7-10 times lesser than typical human reactions so to use and be able to manage movements during that time, 10tman should react at least 10 times faster then average human. To be able tune his movements during the movement itself, I would say, he should be 30 times faster then average human, at least. (100 times and he will be fine, and do miracles)
Less volume room is, less percentage of his ability's 10tman can use. But definitely he can run walls, ceiling(not suspended ceiling obliviously, real one). You can imagine that by imagine average human in less gravity(0.001g) in room where surfaces are covered with ice, but faster you move more centrifugal force it is, less icy it is(and more muddy it becomes), then icy walls breaks. And that all takes 0.1sec instead minutes with average human in icy room.
Needs to add: Probably big volumes are also bad for such action. More you in the fly, more time you have troubles to control your actions-trajectory, and probably wingsuit is a must have item, but jumping of solid surfaces(those which withstand 20-pound cannon blasts, vaults and such) will be more efficient. The action is a combination of both - and actually very complex one. Not all distances between opponents are equally good, depends on the weapon.
Let say some one jumps with speed 44 m/s, at duration 0.02sec it is a travel distance about 1m. Uzi shoots 350m/s bullets, so in a room with distances 20m, as an example, it will take for a bullet 0.06 seconds to cover the distance. And it's not the fastest or most powerful weapon. 0.06 seconds time means - if you can't control your trajectory for about 3 meters - you may be vulnerable to such type of attack(if you against a similar villain, which can react fast enough). If they are vulnerable to the kinetic weapon (and that may be actually not the case - depends on where their strength comes from) then having two one shot gunknifes is a good idea. And all tactics is around how to place good single shoot. Automatic will not work on 100g actions, but it can be used if that's taken in to account, but 1 shot will work at any time.
Actually, close combat isn't a bad idea, because it will downplay many possible weapons and upplay individual characteristics like reaction time, and that is not so much different than usual close combat strategy.
All that wonders 10tman needs only against another 10tmans only. 9t man is no competition for him, 11t man is over powered for him.
The difference in speed of reactions between highly trained man and the average person is actually small. You may google for Isao Machii, he performs some showcases, didn't found original video for pellet cut, they have measured his typical reactions, he was some percents faster than average, but not so much (10% better, something like that, though not sure about the exact number).
So reaction time makes a huge difference in the results, with small changes to it one get a lot of advantages, with the same force. And be able to use full strength in motion is directly connected with speeds of reaction. So 100tman with human reactions is just big stupid rock, definitely, you do not wish to be caught by him, but if you do not do stupid things he is harmless.
Against any human few percents of 10tman ability's is overkill, except snipers, with average snipers involved just move more chaotic and 3 times faster than average human (but not forget snipers are not you enemy, stinger rockets are).
Technology is my god
The problem is a source of 10tman power. How it's done.
I can imagine such 10tman with technology's we already know, but which are not mature enough to do it right now. However, with those technologies, there is no place for fist fights, stuff trowing, skyscraper-jumping. Hulk will be destroyed in time way less than eye blink, like most of them who can't operate time, or be matterless(intangible).
That is just like a note, the source of strength is also important for strategy and tactics of such combat.