Well, your use-case is not in line with the question. You've got the items first, and needed to restart the quest. However, the OP asks for skipping obtaining the items altogether.
As for the items, I can certainly say that you have to speak with the Orc King to be able to use the gemmed lamp in the Djinns quest.
With a knowledge how the quest systems used to work in the ancient times, I suppose it covers at least all the items that you need to obtain from an NPC, and you can obtain them only once. Probably items that update your Quest Log (after getting them) will fit here as well.
What is interesting, you often don't need to have such items with you, as the quest flag is enough. It happens to me a lot, and for instance I have a spare Sarina's vase or some dwarven beards...