What does it mean when a stray cat has a earring on it's ear?

If the cat is truly wearing an earring he must have been some body's pet at some time. Some groups that trap, neuter and release mark the cats so they don't catch the same ones but usually it's by cutting a notch in an ear not an earring. The best way to catch a cat without a trap is with lots of patience. Keep feeding it and move a little less far from the dish everyday until it will let you get close. You have to be very slow and very quiet. Sit and talk to it while it eats, you just have to make friends slowly. It probably sleeps in the tree for safety. You could try making or buying a house for it and put it in a nice safe place. Good luck and bless you for taking in a stray.