If she does not know where the oil is, she searches for the oil. If she thinks the oil might be in the room, she searches the room. You can combine the ideas together to say, "She searches the room for the oil." The room is where she is looking, and the oil is what she hopes to find. You can also just say, "she searches" and not specify what or where.
So "she searches the oil" might be said if she thinks that something she lost might be in the oil. Like a bracelet, as ryan5 suggested. I hope that makes things clearer. (That's the difference in the English. I don't know if that is precisely the same as the difference between "durchsuchen" and "suchen" or not, unfortunately.)