There's not going to be a moment when the world suddenly goes from having oil to having no oil. Some oil reserves are relatively cheap and easy to extract. Other, very large reserves are currently so difficult and expensive to extract that doing so isn't profitable. As the easy oil gradually runs out, the supply drops, the price rises, and sources of oil that were not profitable at the old price become profitable. This maintains the supply of oil and stabilizes the price.
Eventually oil will become so expensive that alternative technologies will be cheaper than it. This will happen with plenty of hard-to-reach oil left. So it's true that the amount of oil is in principle finite, but that limitation isn't really relevant.