Inflation is responsible for an increase in the price of oil or is it that the price of oil is responsible for an increase in inflation?

Yeah, well that's the question, isn't it?

In my opinion, it's the price of oil that is primarily responsible for the price inflation we're seeing, but there certainly has been a pile-up of dollars in the world over the past few years, which means it's probably both.

Or how about inflation is the result of an increase in the money supply?

As an example:
http://www.futurecasts.com/Understanding%20Inflation.html