22-250 is plenty for head shooting, will actually make a mess of the head.
As far as how to hunt them. Here in Texas they can be quite nocturnal. I hunt them at night. I put solar spot lights around the feeder and sit within 75 yds so you can see better, the cross hairs can be hard to make out on a black hog from anything farther than that. Solar spot lights can be had at any home depot or lowes, get the 3 pack and set them up 10-15 yds away pointing under the feeder. Sit and wait 1 hour before dark and as long as you can sit there. I cheat I use a game cam and can pattern there times showing up at the feeder.
Another way is to corn the crap out of senderos or roads and sit and wait, right befor dark is usually when they will come out to feed.
PS the last 10 or so hogs I have killed all fell in there tracks to one shot from my .22 Hornet. Just put it anywhere near the ear and they drop.