First of all....is the table veneer or solid? Is it chipped and dinged or just the wrong color?
If the color is wrong you can always add a tinted varnish, after lightly sanding and cleaning well.
If it's solid I would use a water wash stripper....if it's veneer I would use something that you use mineral spirits to clean off...so you don't lift the veneer. Nothing that will remove polyurethane is non toxic....you need to be outside or have a good ventilating fan.

Most strippers you can find will be methylene chloride. You should definitely use this outside. A semi-paste will give you some time, just don't over brush it on. Less common is NMP. MC will work better but is more "toxic" The biggest mistake is not to give the stripper enough time to work. Let it sit and do its job. I usually put a sheet of plastic over the stripper to keep it from evaporating away too fast.

Unless someone finished this in their hobby workshop, it's likely not polyurethene. It's just not a production finish. More likely for a factory finish is lacquer. I like to use acetone as a rinse as it will also strip off the little residue of finish that might remain. If you want to get it out of the pores, use a Scotch-Brite scrub pad (maroon or light grade) with the acetone. Do not use steel wool for this as the iron in it will react with the tannins in oak and leave black stains.

Tinted varnishes such as Polyshades are terrible products. Very difficult to get on evenly and poor adhesion to most under coats. CIAC.

If you want to reduce the dark-light contrast on the grain, you want to use a dye-based stain, not a pigment based one. Problem is, the yellow cans you find at a home center will not tell you which is it. A real woodworking stores will have liquid or powdered dyes. Otherwise, you have to open the can to check for sludge on the bottom (the settled out pigment)

I'd recommend getting Bob Flexner's "Understanding Wood Finishing" at your library or bookstore and reading relevant sections of stains and varnishes. It's a great book.