There’s an interesting article by Elliott Gue at Seeking Alpha on whether the dollar drives oil prices. Skipping to the last chapter, the answer is that the exchange rate is a factor but it’s not the most important factor. 90% of the changes in the price of oil are explained by factors other than the dollar.
That raises the question what does drive oil prices? I can only offer guesses. My guess would be that short term movements in oil prices are influenced (in descending order of importance) by supply and demand, speculation, cartel pricing, and the value of the dollar.
Anticipated future demand/supply and actual present oil prices on the spot market is what drives oil prices. Most oil is bought and sold as futures contracts, and few of the purchasers can take delivery. If the purchaser of a future contract cannot take delivery, he/she must sell it or store it.
In addition to using storage facilities and tankers, one storage option is to store it in the ground instead of pumping it out. Now there is the storage cost that must be included.
If the anticipated future demand is less than the actual demand at the delivery date, the oil must be sold at the price for present demand (spot market). If the future contract was purchased on margin, there will be a margin call when the value drops, and this adds additional downward pressure.
In addition to fuels, heating oil and plastic are other products from oil. While oil costs are a component of gasoline prices, gasoline (and other fuels) are priced on the present supply and demand, and because they have storage facilities, refineries have more options. They can store the more expensive oil and use cheaper oil to produce products.
There is also another factor. Oil is sweet or sour, and this is determined by the sulphur content. Sweet oil is used to refine fuels, and sour oil is used for plastics. Shale oil is sweet, and middle east oil is sour, and it is possible to have a glut of one but not the other.