It might be worth checking out the subfloor if you can get access to it in case that is what is not holding up to weight instead of the joists.
Otherwise, I know in your comment you stated that you don't have the joists exposed, unfortunately, I don't know of a way to resolve the issue without exposing them as anything you tried to do at the floor level would just be adding weight.
If you don't feel your joists are up to snuff, you can reinforce them by laminating them.
You would get additional boards of appropriate size to fit snugly next to the joists, then use an adhesive and screw the boards to the joists.
Make sure you are getting the additional wood over your load bearing walls, otherwise again you are just adding weight to the situation.
Remember though, even if you are going to make it a DIY project, structural work is a big deal and you should at least consult a contractor/architect and make sure you get proper permits and inspections.
You can save yourself the money on the labor, but don't skimp on the planning.
It sounds like the joists aren't properly fixed to the walls or they aren't big enough for the task at hand - keeping your floors up.
I'd get another builder in to take a look and quote for remedial work and then try and get the first builder to either sort out the problem or pay for someone else to do the work.
Best Answer
I won't suggest a brand in particular, but there are commercially available cleaners meant specifically for stripping hardwood/pergo/laminated flooring. A quick Amazon/Google search for 'Floor Polish Remover' brings up many options. It appears that this could be quite the project.
It appears as though some people also use a large rotary floor buffer/polisher to even out/remove any waxy buildup. This could also be a 'Pro Project' or something you could contract out.
Good luck.
(P.S. Whatever the outcome, I'd be interested. I also have hardwood floors that may need to be stripped)