Adam Ozimek helpfully summarizes some research on the elasticity of the demand for oil and gasoline:
Two points about this kind of thing in a tax policy context that I think often go overlooked. One is that while low elasticity implies that a tax is unlikely to be very effective at reducing demand, by the exact same token a low elasticity implies that taxing whatever it is you’re proposing to tax will be a very efficient way of raising revenue. So if you’re the kind of person who believes the government should raise revenue, then there’s really no possible result in the elasticity literature that should make you hesitate to tax gasoline and/or oil.
The other thing is that these elasticity estimates generally imply that the relationship between price and demand is going to be linear, which is almost certainly false. Which is to say that the estimate is only reliable when you’re considering a relatively small policy shift. Nothing wrong with that, there’s just no way to get an empirical estimate about some crazy shift outside the realm of ordinary experience. But it is a real limitation to what this kind of work can tell us.