Why the shark liver is so large and oily?

Oil is stored in shark's livers because livers store oil (or fat). When vertebrates digest food, the food does not go from their intestine to the blood stream but to the liver which decides what to do with it. That includes you.

The liver sends some food directly to the blood stream. It gives some additional processing, and rather that release all the food that came through the digestive track at one time it stores some. (Besides that it serves other functions.) If your body suddenly needs more fat than usual, your liver will release it. If the need continues for any length of time, your body will instruct your fat cells to start releasing fat. Sharks work the same way.