The reason your research seems to cap at about 3-4x strength is because that is about the theoretical limit of biology based on what we see in other animals of similar size to our own. That said, 10x strength is doable without magic if you get into cybernetic enhancements. An electric motor the size of your bicep can pull hundreds of pounds of force quite easily. If you attach your motor to a transmission system, then a cybernetic limb can scale torque in a way biology can not so that you can slow lift absolutely incredible weights with little extra total strength needed; so, a person whose body has been surgically augmented and reinforced with machinery could obtain at least 10x strength no problem.
Cyborgs come with many caveats
Biology becomes your weakest link: If you want to pick up 500 lbs with one hand, you need to reinforce everything from you hand up your arm and down your back all the way to your feet (and possibly even the floor you are standing on); otherwise, a single wimpy organic chunk will become your weak link that breaks under the force. Such a cyborg would likely need their outer torso, and all four limbs completely replaced. The head, spine, and endocrine system needs to remain in tack though for this "person" to still think, perceive and feel like a human. You digestive tract, pulmonary, and respiratory systems will also need to be left at least partially intact to keep your organic parts alive.
Cybernetics are foreign bodies: You will also need some pretty serious anti-rejection augmentation to prevent what is left of the body from rejecting the cybernetic parts. Anti-rejection medication weaken the immune system, and would likely not do the trick for such an advance cybernetic integration to work. This is where your biological engineering skills become important because you'd have to reprogram the immune system to accept the extensive foreign bodies without weakening it against infection and bleeding out.
You now have a two sets of needs: Your body parts that are left will continue to need nutrients that can not be delivered by an electrical system; so, you will need to continue eating to keep your organs alive, and your super strong mechanical body will need a strong electrical power source, lubricants, replacement parts, etc. that the body cannot produce. This can make surviving in hostile environments far more problematic for the cyborg.
Newtonian Physics: Just because you are 10x as strong does not mean you have 10x as much inertia. When a 200 lb person pushes a 100 lb piece of furniture, the furniture tends to move because it has less inertia/friction to overcome. But when a 200lb cyborg pushes a 1000 lb piece of industrial equipment, the equipment may stay put and the cyborg just gets pushed backwards. This means workplaces may need specialized foot-holds and things to brace against if you want your workers to be able to exert their full strength to any effect.
High torque may be strong, but not fast: If your cybernetics rely on torque adjustments to lift greater loads, this means that you slow down in proportion to how much you speed up; so, lifting 1000 lbs over your head may not be too hard, but throwing it might be impossible because you can only lift that weight when geared all the way down. If your cyborg wants to throw, punch, run, etc. He may need to gear up and do that at much closer to human-like strengths. Where mechanics are concerned doing both strong and fast requires a lot more power and therefore bigger motor systems that may not fit in your human sized cybernetic chassis.
Looking human: As long as you are taking out human parts to replace instead of just building on top of them, your overall frame remains the same. As for skin, you could theoretically graft human skin over the cyber parts like a terminator, but it may tair too easily under such conditions. As long as you just mean looks mostly human, then the cybernetic parts could be hidden under kevlar reinforced polymer synthetic skin, or you just hide those bits under clothing.