Do you know what the stain color is? You could tape off an area that might be less conspicuous, along a seem, sand lightly, stain and use a solvent based polyurethane ( since you don’t know what’s on the floor).

I don’t know what the stain color is, but I’d be willing to go a little darker if it would help conceal unevenness. Is there a certain type of stain I’d have to use? What is a solvent based poly? Sorry, not that familiar with the process.

Stain alone (gel stain or regular) will not protect anything, stain is a colorant essentially. And poly or any type applied over the floor in its current state will be good money after bad. And any of those floor wax type finishes will do nothing but ruin the floor so you may not even be able to refinish it.

Put down a rug or floor cloth and protect them from any more abrasive traffic. Until you get them refinished, any traffic over unfinished wood will grind in dirt, and create bigger issues for the refinish.