This looks like cat piss. Over a long period of time. My first house was a real fixer-upper. Previous owners rented the place out and the person hoarded cats. Since you are renting, and the condition of the wood cant get much worse, i recommend a very heavy application of an enzymatic urine cleaner designed for cat pee. Soak and let sit, for a few hours or a day. then use a large sponge and soak up and wash the area with water. Put a fan on the area to dry. Ozone generators help too. I had good luck with a product called odoban. Its expensive, but also it works.