How sharp of a turn are we talking about? Turn foull to lock and it will do that as the axles are binding a bit. Are we doing this on a hard dry surface or soft or slick surface??
Sorry for the above short answer dennis2, I had to go and give my dog an insuline shot....
When you put your truck in 4wd, you lock the front differential together with the rear through the transfer case.
To explain this you have to imagine an overhead view, looking down over your truck. When you put your truck in a tight turn, the front tires are making a bigger circle than the rear. When you have it in 4wd on hard dry pavement and turn a tight turn, your front tires are traveling a farther distance than the rear tires. What you're feeling in the steering wheel is is as O'Rattlecan described in an earlier post, wheel hop, where the front tires are fighting the rear.
I hope that explains it somewhat to you.
BTW, I sure didn't mean to forget, welcome to our site. Make yourself at home here and please post up and post often. If you like what you see here, tell your friends.
Oh, I almost forgot, congratulations on the new 2008 f250. If ya get a chance, post up some pictures and fill us in on how you like it etc.
But that doesn't mean it's good. Don't drive in 4x4 on pavement. It's not designed for it, and it's not good for it. That "vibration" you're feeling is putting a lot of stress on drivetrain components.
*Like a lot of things, you'll find guys who swear they've done it for years and never had any problem. Me, I listen to my friend with 300k on his F-350 (no drivetrain repairs except the clutch), and he says don't do it. Don't worry about having damaged it from what you've done, but try not to do it again.