Soil Toxicity

I live in San Diego, and although it normally never rains, this past year or two has had a lot of it. We have around 10 cats. We keep their litter pans outside in a cattery (a large cage that connects to our house through a window). Every time it rains the litter pans flood, once we put 2 tarps over the cage completely covering it and they still flooded. Every time this happens I have to go into the cage (it's of a size that we can walk in it), drag out the litter pans, and dump the water out.

The liquid in these pans is nothing short of radio-active. By the time we can get to them the rain water has already been sitting in the pans for about a day or two, absorbing all the urine, fecies, and kitty litter. I fear that if I ever accidentally swallow this stuff i'll get cancer and die. Naturally, since this stuff goes into the ground, i'm worried about soil toxicity. The cats we keep outside (because they don't obey the inside rules) also like to poo in the ground, along with the dogs we let out occasionally.

The ground was never healthy to begin with, even when we first moved in 9 years ago. My younger siblings have been digging holes out there in random places since we first moved in, and have been digging up toys, clothes, and other random objects long since forgotten in the ground.

We also have a major weed problem. When we first moved in the yard was nothing but dirt, then there was grass for a while, then the weeds invaded. We've been fighting the weeds for about 3 or 4 years now. We go out there and pull them up by the roots and dig up the soil around them, and it's been getting better. It's nothing like it was last year (I went out with a hoe and a machete, the weeds I were killing were taller than I was), but it's still not as good as I want it to be.

I want a garden, for plants, vegetables, and fruits. How can I make my yard healthy, and check to see if it's safe to plant edible food?