My best friend is working a seasonal job with KY Fish and Wildlife and his entire job is killing hogs. He uses Corral traps as described above baited with regular corn and sour mash. These traps are very effective and you normally get a multiple catch.
Setting out snares on some travel routes or around bait can be very effective as well but you have a lot of traps to check (unless you are gonna leave them and let the coyotes eat them...not real ethical but hogs are worse than rats so kinda hard to feel bad for them).
You can also try hunting them but this is the least effective means. This is especially true if you use dogs because all it does is push the hogs into a larger area.
No matter how you try to kill them (corral, snare, hunting) they get VERY wary of human scent. If you are going to trap, I suggest that you wait and try to trap when conditions get the hardest because it will concentrate them around the bait you are putting out.
You might also want to call your state agency or USDA officer for your county/area. With my friends position you can enter into an agreement to pay X amount to help them build the traps. After that the official will bait, set, and clean out the traps for you.
Best of luck in eradicating them