re: urine in hardwood
Stains are one issue, the urine smell is the other.
You can try to neutralize the urine with an enzyme product (Nature's Miracle is what I've used for various stains and odors, but not on urine that has soaked into a hardwood floor), but that may or may not work.
After neutralizing the actual urine, then you can maybe attempt to bleach out the water/ammonia stains (from the urine and then from the water-based enzyme neutralizer products). Wood bleach (oxalic acid usually) and/or hydrogen peroxide are two common wood bleaches (do NOT mix them! They are two DIFFERENT bleaching products, you would use or try them separately.)
And if the urine has soaked into the seam between boards and/or otherwise gotten down into the subfloor, the only real fix is to remove and replace the urine-soaked areas. IMNSHO
(surface staining is one thing and bad enough, but unless you originally cleaned up the urine almost immediately you are almost certainly dealing with urine that has soaked into the wood and will really NEVER 'go away' no matter what you do to it short of remove and replace)
Applying a polyurethane varnish over an oil finish may be iffy. If you sand far enough to completely remove all of the old floor finish, then you should have no issues.
If the oil finish was a "drying" oil, then you should have no compatibility issues with top coating with a polyurethane varnish. Test first.
Your bigger concern with the old floor oil finish is probably the buffing wax or silicones that may have been applied. Those for sure will mess up any attempt to top coat or recoat with any varnish (polyurethane or whatever).
But what you can usually do if dealing with possible incompatible finishes is to apply a sealing coat (or 3

) of shellac. Within limits, shellac sticks to almost anything and almost anything sticks to shellac (with regard to finishes). Shellac by itself is not all that durable, especially for a floor finish, but it MAY be just durable enough to let you get a successful bond between the different finishes (old oil in/on the floor to shellac, and then the polyurethane to the shellac).
Test first and maybe reach out to the floor varnish maker(s) and their tech info (chat, call, email, carrier pigeon, etc).