Decided to break out the Deodorizing section because there could be so many situations and surfaces involved.

One word--- Odorcide. 

There problem solved..... well at least some of them.   

See? This is what I am talking about.

Get a dog? 

Paint the floor with some stick-em.  He wont like walking on it any more. 

Of course you won't either, but that wasn't the question.

Some "neighbors" here have lost their cats to these animals. They eat almost anything from what I've heard?

I saw a coyote crossing the street with a dead cat hanging from his mouth. I'll see a flyer posted in the neighborhood looking for a lost cat from time to time. What was the original question?

Getting rid of the cat is like saying get rid of your children, sometimes she pisses me off(only the pee issue)...but this just recently happened.  Before she would always use the litter box, never had any issues and we've had her for 10 years now.  I used some alkaline, let it sit, than used some lovely cotton pads and skated around in them.  I knew they were good for something!

Cotton pads - great for urine removal from your tiles.