I've heard that a product called "Nature's Miracle" (which can be purchased at many pet stores) works very well at removing pet urine odors.
You should also be aware than all mammal urine fluoresces under ultraviolet light, and that professional cleaning contractors use black lights made specifically for locating pet urine stains to find and treat pet urine odors.
Bane-Clene® Ultra-Violet Black Light Pet Urine Detector
Bane-clene is a well respected name in the janitorial service sector of the economy.
This web page caters to the janitorial service sector:
http//:Cleanfax Online :: Brought to you by Grand View Media
Type "black light" into the search engine on that web site and read some articles on using black lights to find and eliminate pet odors.
I'm thinking that if the urine smell is as bad as you describe, then refinishing the hardwood floor might not be an option available to you. You might have to tear out that hardwood to remove the smell entirely from the house. I've heard of cases where the pet urine penetrated so deeply into the floor system that the home owners had to remove the carpet AND the plywood underlayment in the house to eliminate the pet urine smell.
If that turns out to be your only option, then keep in mind that some high end carpet underpad is sold as "pet pad" because it's made by blowing the rubber with less blowing gas so that the bubbles inside the rubber underpad don't interconnect. That makes the underpad impermeable to pet urine, and should also help prevent pet urine odors in the living space of the house.
But, I should also admit that I don't have any personal experience doing this sort of work.