They are just dinosaurs! They were planted by the Nebraska Game and Fish department because they're a native species (as opposed to pheasants). Now they're everywhere in Nebraska, including well into the city limits. They destroy the upland game populations by eating the eggs and chicks. You should run over, or by any method, kill every wild turkey you see. Me and my hunting partners harvest as many as legal. On city birds you can do it with a 9-iron. Wild birds easily call to decoys during the strut. Don't leave the carcasses lying in the fields. It'll cause the coyotes to breed extra litters.
Now...to the question of taste. We only eat the breasts which are not nearly as large (or as tasty) as domestic birds. I think the best way is diced and cooked stroganoff-like over rice or noodles.
Bentley, get a scoped .22 rimfire and thin that flock—they've been breeding like crazy!