How much surface area do you really need to hang drywall on studs? I received a shipment of lumber, and most of them have wane on both edges of the studs, which means I can't "bury" the wane on the non-drywalled side. I think a little bit of wane should be fine, but at what point will the drywallers not have enough width or depth to hand their drywall?
I generally agree with Ed Beal regarding lumber quality. My personal standards wouldn't allow use of such lumber. Regarding your question...
For field studs, as little as half an inch should be fine. Much smaller than that and the sheet will begin to deform around the sharpened edge of the lumber when the screws are set, causing waves in the wall and weakening the sheet.
For edge studs, I'd want at least 1/4" under the entire length of the sheet end for the same reason: The edge of the sheet will buckle when it's screwed to the framing.
"Wane" is the area on a edge of a board where the bark may have been but flaked so the edge is not a full flat surface. In today's high recovery saw mills the lower grades may have wane on all 4 sides of a 4x4" because the tree top was not much larger than that. Not all lumber is safe for building it should have a stamp on it stating the grade. In my state #2 is the lowest grade for structural lumber and the wane is limited to get this stamp. It sounds like you have #3 or #4 grade lumber I would check local building codes to verify it is safe to use. I will double check with one of our graders on the limit of the wane for structural lumber. I just talked to our planer operator he grades on occasion he said 2/3 the wide side can have wane and 1/3 on the narrow but the other 2 faces should be clean for a #2. He did say there was a small % that can exceed this but we don't push it or we could loose our stamps. The inspectors regularly pull loads and inspect complete units of lumber with the grader.