Reinforcement Oil protects your item only when you drag it into the protect slot of the Reinforce window; in the inventory it does nothing.
Where supplies come from
Oil and Reinforcement Stones come from dungeon final bosses (a Reinforced Stone Pandora and a chance of Oil), rare named monsters, weekend invasions in Pampus and Earis, attendance days 5 and 21, battle pass free tiers 8/18/28/38, and Golden Bell and Puzzle Challenge winners. They are not sold in the Item Mall.