Never harm a cat in your neighborhood. Animal cruelty is a felony in many states.
Never offer a cat "free to good home" in the newspapers. Dog fighters sometimes get "bait" animals from these ads and will use cats and kittens to bait their dogs for fighting. They acquire these unfortunate animals from "free to good home" ads. Always ask for a fee. If you like the potential adopter (get references) you can always waive the fee.
The problem of feral and homeless cats in America is a big one. Tragically, shelters will not take feral cats because they are not adoptable. Feral cats are not strays, but cats who have never had a home and whose ancestors have never had a home. Stray cats are those who have had a home but for one reason or another lost it. Try to see things from the cat's point of view. They didn't ask to be homeless in your yard. But if you want to get rid of them, do so humanely.
Install motion sensing sprinklers. HavAHart, (HaveAHart.com) the makers of the humane trap, also make a sprinkler system that turns on when it senses motion. Cats do not like water and will run from your yard. A random spray pattern keeps cats from figuring out where the water goes. There are similar products manufactured under different brand names.
Set up a humane trap. If they are feral or stray cats, Alley Cat Allies suggests you trap, neuter and release them, or TNR. Catch them in a humane trap and take them to the local shelter or animal control facility to be spayed/neutered. Then they can be re-released back in your area, where they can live but not reproduce, or released into another feral cat colony. In the absence of any active TNR programs in your area, the cats will simply be euthanized.
Place an ad in the paper, on Craigslist or use other resources to find someone to adopt the cat. If the cat you are trying to rid yourself of belongs to you or has adopted you and you cannot keep her, find her another home. Take her to the vet, have her tested for feline communicable diseases and, if she's healthy, have her spayed (neutered for a male) and try to find her a home. If you can't be her owner, be her friend and help her find a home.