The "oil just up and vanishes" scenario is interesting, but ultimately useless, as the result of that scenario has no relation to what will actually happen as the natural sources of oil are used up.
As more and more oil deposits are used up, new ones become increasingly hard to find. Not impossible to find, because resources don't disappear overnight, but it does result in the process of finding oil becoming increasingly expensive. An increase in price usually leads to a drop in demand, but that doesn't happen with oil for the simple reason that it's still the cheapest, most convenient option. Substitutes exist, but they're more expensive and typically unavailable in many areas.
But eventually the price of finding new sources of oil will reach a point where using one of the substitutes becomes cheaper. As this happens, existing companies will remodel themselves and new ones will rise in order to distribute the existing substitutes, simply because they can now produce them more cheaply than oil. Since they'll be cheaper, customers who are not inconvenienced will start to switch over to the substitutes. This will put more money into the substitute companies, allowing them to expand and solving the convenience issue. Competition between companies will lead to R&D in pursuit of making these substitutes cheaper to produce, in order to undercut the prices of their competitors.
This is a ridiculously simplified market model, but I think it's an accurate depiction of the scenario.
I'm very sorry for being a colossal bore, but you read to the end of my post, so you really just brought this on yourself.