I understand your doubt and I'd love to know more about that number myself.
I suppose it's possible to come up with such a number by including every income tax deduction that oil companies might take, like the salaries of their employees or capitalized expenses. Of course, every other business in America takes similar deductions, so it's not really a subsidy.
There are a lot of ways that we subsidize other forms of energy though. How many military efforts and how much politics is involved with keeping the oil flowing from the mideast? There is a commercial on TV that says that if you do drugs you may be subsidizing terrorists. That same commercial could easily be done showing that if you use gasoline you are subsidizing terrorists.
Natural gas and coal seem to be the only ones that don't get subsidized very much.
It's an interesting question, and I've seen it raised several times here. It doesn't have a rational answer, though, because you can't allocate a specific percentage to those efforts. Additionally, everyone benefits from an abundant oil supply, so I suppose one could argue that consumers are having their gasoline purchases subsidized, or that it's really a subsidy to the airline industry. That line of thinking simply doesn't lead to a conclusion that's worth anything for comparative purposes.
An Arctic drilling tax credit (which doesn't exist) would be something that is easily measured, just like the farm subsidies, or even the duties imposed on Canadian timber. But the $36 billion number is mighty suspicious.