If you already have one of the items needed for the quest in your possession when you reach a step, you can get the quest to update by selling an item to a vendor and then buying it back. Conveniently, there is a vendor Sage Elrendir located just inside the hut next to Elowys.
You must return to Elowys with the item in inventory to complete each step of the quest. If you do not have the item in inventory (ie you sold it) then she will not update the quest.