Dog odors, cat odors, and other animal odors can be cleaned using white vinegar and water, and later use a solution of T.S.P. (trisodium phosphate) and liquid bleach. Pine Power or Lysol is for a final disinfectant. Then finish an air-fresher spray.
One of the oldest recipes for cat odor like urine removal is to mix white vinegar (1 part) to warm water (2 parts) and apply the mixture to the area for about 15 minutes. Rinse and let dry.
For a second round, try a solution of T.S.P. (trisodium phosphate) and liquid bleach to sterilize and help remove the stink. For dog odor and other animal odor, make sure there is not any urine left on the floor when using the bleach. The ammonia in the urine and the bleach could produce a poison gas.
Mix a quarter cup of T.S.P., a quarter cup of household bleach to one gallon of warm water. (Be sure to wear protective gloves and clothing when using a strong solution of T.S.P. Also, test the flooring to make sure the mix does not harm it.)
Apply the mixture to the floor with a sponge mop until you have covered about a ten by ten foot area. Then go back and reapply over the same area, possibly a third time, until it looks clean. Part of the multiple applications is to let the T.S.P. loosen up the dirt, the other part is to let the bleach soak into cracks and crevices and disinfect any spores, fungi, and such.
After phase 2, use Pine Power or Lysol on the walls and floors for a final disinfectant. This should leave the basement smelling ‘fresh as a daisy’ by now.
Then use Odors Away, Smells-B-Gone, or Febreeze, and spray liberally up on the floor joists and everywhere you were not able to mop and wash. These products react with odor causing molecules and break them down. They do not just mask the smell, but eliminate the odor.
Another tried and true smell eliminator is to get an ozone air purifier (rent or buy) and let it run in the basement for a couple of days. The extra oxygen atom from the ozone attaches itself to stink molecule and breaks it down to simpler, not stinky, molecule. These work so well for us we rent them with a money-back guarantee and have yet to get a request for a refund yet.