What should I do with The Treasures of Meropis?

Given that all the other quest items in the game, even the ones for quests you don't have yet, seem to be unsellable, I think it's safe to sell these off. Some Googling backs up the idea that they aren't used anywhere else:

Once you collect all five treasures scattered over Dalentarth (track the mission and see the locations), you complete the mission. Sell (or stash) all five if you like; they are worth roughly $800 per item (with no Mercantile skill increase).

On a related note, I tested and you can actually sell them off while the quest is still in progress. It's finding them that triggers progress and completion, not possessing them. So you can sell them off as you go to free up inventory space and the Treasures of Meropis quest will still complete. There is no need to wait until the end and sell them all at once.