You can try Nature's Miracle brand odor-remover- it's in most major pet stores and it claims to neutralize cat pee odor with enzymes that counteract the proteins in cat pee that make it smell so incredibly horrible. It's not perfect, but it helps.
I feel your pain. I used to have a cat who I loved and doted on, but she developed a serious kidney disease and couldn't make it to her litter box in time on a nearly daily basis. It broke my heart watching her sick, while causing my husband and I much discomfort and embarrassment- We felt like we couldn't even have friends over anymore, the smell was so strong. I had to get rid of some of my favorite pieces of furniture after going so far as having parts of one beloved, vintage chair professionally cleaned, tossing its cushions and having a foam/reupholstery place cut new ones, replacing covers, and yet still, the pee smell was in the back of the chair because my car would often be sleeping on the chair, suddenly need to go, and spray urine on the chair back when she got up, making even reupholstery not a great solution. When I found Nature's Miracle, I found that it did make a noticeable difference, but I still had to jettison far too much that was beyond saving. My cat eventually passed away of old age after we put up with this for many years, and we've since moved out of the house where she lived most of her life. Another thing I'm not clear on- You make it sound like cats don't live there any more, since you say "the cats that once lived here," yet you mention there's still cat hair in the house. In that case, it sounds like there's car hair in the heating ducts/ventilation system, which is not uncommon. It's worth hiring a duct-cleaning company to vac that stuff out! We did that shortly before our daughter was born and it was very worthwhile. Good luck!