What I did to fix my cat odor problem -
I have a cat who decided to use one corner of our living room as an extra potty. She has been doing this for over two years. I periodically had the carpet professionally cleaned. The cleaner pulled the carpet up and cleaned the pad as well. For a while, this method worked well enough. Our house didn't stink all the time. I also used an enzyme product called Bi-O-Kleen Bac Out Stain and Odor Remover once a week.

I decided to pull up all the carpet and install a floating hardwood floor. After I pulled the carpet up, I discovered that the urine had soaked into the concrete. Concrete is a porous material (notice how it changes color when it gets wet outside, that's because it soaks up water). I will detail how I managed to get the odor out below, noting what worked and what didn't work:

a) Bi-o-kleen Bac Out Stain and Odor Remover. I sprayed this product onto the concrete hoping it would soak down to the cat pee and get rid of it. No such luck. I tried twice, the second time really soaking the concrete.

b) Baking Soda. I bought the biggest box of baking soda I could find (about 8 times the size of a regular box) and poured it over the concrete. I left the soda sit for 24 hours, then I vacuumed the area. I couldn't tell any difference in the odor.

c) Ozone generator. I used a plastic drop cloth to close off the living room area from the rest of the house. I did three 1-hour shock treatments of ozone (please read the notes on ozone below if you decide to use this method), then a two-hour treatment. I put high-powered fans in the room and aired it out for hours in between. This helped a lot! However, there were two small areas that still smelled like urine.

d) Vinegar and enzyme stain and odor remover. You have to neutralize the urine with vinegar before the enzyme cleaner will work. I tried this. I did not notice an improvement.

e) Natural Solution stain and odor remover (from Trader Joe's). This product worked to get the rest of the smell out (at least I can't smell it. It's possible that the cat can still smell it). This method took a long time to dry out (I used a non-puncturing moisture meter to make sure the concrete was dry before I sealed it).

f) AFM Safecoat Safe Seal. I used this product to seal the concrete and (hopefully) seal any remaining odor in the concrete. Only time will tell if the cat can still smell it. If I had two weeks, I could have used a Timber-Tek product which soaks into the concrete and pushes out impurities, and then seals the concrete against moisture. But this product has a 2 week curing time. I was too impatient at the time, and perhaps a little skeptical that it would work completely. If somebody out there has experience with this product, I'd be curious to hear how it worked out for you.

Notes on ozone:
Don't have anything that is alive in the same room as the ozone generator. It will kill plants and animals. Try to avoid inhaling it! There are some dangers associated with ozone, it's known to bring out formaldehyde and other aldehydes in the area. There's also a concern that the ozone allows other chemicals to bond, producing things we've never seen before and that are potentially toxic. This is why it was recommended to me that I do 1 hour shock treatments and blow the area out using fans for several hours afterward. It was unrealistic for us to do a 36 hour ozonation, though I'm curious if that would work.

Notes on cats urinating outside the kitty litter:
Cats don't pee outside the kitty litter out of spite or anger. They may have smelled some previous pet's urine and decided to pee there. In the case of my cat, the veterinarian thinks she has a problem with crystals in her urine. That veterinarian recommended exploratory surgery, which I declined. I've been doing some research lately about this problem of crystals in urine. It may be Feline Urologic Syndrome (FUS), aka cystitis. According to The New Natural Cat (by Anitra Frazier):

"These crystals are sometimes called sand or gravel. They are made mostly of magnesium and phosphorous that have been ingested in the diet as ash. Dry food and fish are high ash foods that should be avoided. Other factors that can contribute to the problem include an alkaline urine. The cat's urine should be acidic; the crystals will dissolve in an acid urine."

She has some suggestions for how to make the cat's urine more acidic, including supplements and special food and feeding only twice a day. What my veterinarian told me is that these crystals cause urination to be painful or uncomfortable, and the cat associates the pain and discomfort with the litter, so the cat finds a different place to go.

Obviously a clean litter box is very important for cats. I used to be pretty lazy about the litter box, but I've found a litter that works pretty well for me now. We use unscented XXX, which clumps, but is also flushable. We have a kitty litter box next to each toilet, and we scoop every day, right into the toilet. My husband scoops one litter box and I scoop the other. The New Natural Cat book recommends a non-slotted large spoon to do the scooping. Using this spoon you get all the wet urine at once, and the litter lasts much longer. I'm going to get some non-slotted spoons instead of our scoops.