Thanks for all the kind words.
Here is the latest. I picked up the cat at the emergency vet this morning. The girl at the clinic named her “Mystery.”
I walked around the neighborhood trying to find to owner. I had no luck, so I took her to the vet and got her some pain pills and antibiotics.
She has two deep puncture wounds in her right hind leg. She is walking around better, so the vet doesn’t think she will have permanent damage to her leg. Mystery is resting peacefully in the closet in the spare room.
We have three other cats, all male strays, and they are leaving her alone which is a little surprising. We would love to find the owner or a good home for her, but if that doesn’t work out, I guess my wife will have another girl to hang out with around the house. 
I am also very thankful for both the emergency clinic and our regular vet for giving us discounts. The clinic took off 50% from the exam fee and 50% off the board fee and our regular vet just charged us for the pain pills and antibiotics. She waved the $50 exam fee.
As a strange side note: I think Mystery might be the mother of my other black cat, who we found cold and wet under our steps five years ago.