We caught a stray kitten once. We used a little trap. It is basically a cage 6 inches wide by 6 inches tall by 2 foot in length. The door on one end is attached to a spring, so when an animal (hopefully the cat you are trying to get) touches the food at the back, the entry door closes. The principle is like a mouse trap, but the animal is not touched by any parts, just the "box" is closed. I will see if I can find a picture of it on the net.

One other suggestion, would be once your cat has gone out for the night for the last time. Tape a ruler or piece of wood on the cat flap, so it will open in, but the ruler stops it from opening to go out again. Thus trapping the stray inside.

Let us know how it goes in your attempt to catch it.