Due to their mobility, relocation of wild turkeys is only practical when turkeys need to be rescued from life-threatening hazards.
Many states prohibit the translocation of wildlife, including wild turkeys, for humane and public health reasons. If translocation is legal, move turkeys to suitable habitat at least 10 miles, preferably across major barriers such as bodies of water and mountain ranges to reduce the likelihood of their return.
Euthanasia by CO2 or cervical dislocation is suitable for wild turkeys. A properly placed shot is an option considered as humane killing.
Check your state regulations regarding disposal of carcasses.