Oil can come from many sources.
That doesn't change the fact that it will become more scarce in the future. The whole idea of "peak oil" comes from the established fact that oil production has in peaked in the United States. It is expected to do so elsewhere as well.
When it does, the price will inexorably rise. Other factors affecting the price of oil include the value of the currency used to purchase it, delivery lead-time and the resulting speculation on supply & demand, natural disasters, politics, price fixing, etc.
At some point, people will decide that certain oil products are no longer worth the price. People being very much like-minded, they will probably decide this at very similar times, en-mass. If the public uproar over the price of oil over the last couple years is any indication, the critical price might be $145 per barrel that triggers a mass technological shift in demand. Or it might trigger a roller coaster effect, with some people hanging on indefinitely in a gradually dwindling segment of the population that cling to an old technology.
My opinion on nuclear fusion is skeptical. Even if peak oil happens 100 years from now, or 1000 years from now, it doesn't mean that nuclear fusion will replace it as a primary source of energy. Nuclear fusion might not even work.
Demand will be suppressed if other energy sources can't be found. Technologies that don't require as much power will be used. We're seeing some of them already, as prototypes.
Another resource that might be analogous to fossil fuel, is fossil water. This water that comes from underground aquifers and used for irrigating crops. It is also a limited resource. This image shows circular crops grown, each centered on a fossil water well in Libya. You can see many that have been abandoned as the wells have dried up. The only difference between water and oil, is that when an oil well dries up, the pump stops. This isn't visible using aerial photography, as it is with fossil water agriculture. But I assure you, in the United States and elsewhere, many oil wells are also drying up.