Hi S., There are a few things you can do. First you need to clean the basement completely and make sure you don't have any mold growth or dampness. (If you do you need to treat that right away!) To remove the smell of cat pee you should use a mix of white vingar and water after you mop with hot soapy water & it dries. Yes, a dehumidifier will help get rid of the "basement smell" by removing humity from the air and keeping air circulation going in the basement if you center the unit & have a unit big enough for the space. You do have to remember to adjust it in the winter when a house is normally drier. We bought a unit for our first house and that really helped! Also don't forget to change the filter in your furnance at least once a month if you have a forced air unit.
If you have a cat that isn't using it's litter box correctly there is usually some sort of problem associated with that, maybe instead of one cat pan you need two. Or your cat is sick and trying to tell you! Good luck and best wishes.