Why does my truck pull to either side when driving Steering wheel at times rocks

Has to be worn parts somewhere in the front suspension as stated in earlier comments. You need an experienced tech to hoist the vehicle correctly and inspect before you loose control and hit someone. If you want us to check this out please call (313) 208-7752 or schedule an appointment on line at StansGarage.net. I am sure we can diagnose your problem and give you the answer you need. Larry

check all of your front end components for wear and also check your tires

Have a competent EXPERIENCED alignment tech check it for worn linkage , might be easier for them to spot something that they are used to seeing , even though it may not initially look bad.-?

My Truck did the exact same thing! The Majority of the 2004-2008 Ford F-250 super duty diesels do. Ford sent me a letter warning me about the shaking (AKA "death wobble") of the truck. They said when it starts to shake or wobble to apply the brakes until the shaking or wobbling has stopped. Then resume driving. But, there is no Permanent fix. The Problem has to do with the frame and something that is welded on to it.lol I can't remember exactly the name of the part. But, I took my truck which is a 2005 Ford F-250 Super Duty Diesel to the ford warehouse in my town. They had to replace the entire front end of my truck. Which has temporarily fixed the problem for now.