Leaving a quest item on a corpse is a potential game-breaker, so it's safer to loot the corpse and dump the items on the floor, in case you ever have to go back. The corpse will disappear after 3 days, but the items will remain. Selling a quest-related item may or may not be a problem, because in some cases you can buy it back, but not in all. If the merchant equips it (fixed by the Morrowind Code Patch), you might have to resort to killing the merchant to recover the item, or if it's not equipped and their inventory resets at some point (which varies from case to case), then it's gone.
A few of the quest-related items are "named", as in "So-and-so's Trinket", so it's at least somewhat obvious that the item is either stolen or unique. In a lot of cases, "named" enchanted articles spawn as random loot, so it's not always apparent that something is truly unique, but you might want to hold off on selling them unless you spot a second item of the same name in loot or for sale. Most (but not all) unnamed quest items can be replaced or substituted with generic items, so if a TG quest calls for stealing a generic item from a target, you could just buy one to satisfy the requirement. In a few cases, the specific item from a specific place MUST be used, but it won't "stack" with the generic item, either in inventory or storage. I suspect that in 99.9% of the case, socks, rusty armor, and such will NOT be quest items, so you may still be good so far.