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I look at oil as sort of like earth's batteries, where it's stored the accumulated energy of millions of years of sunshine (if you believe the dead dinosaur theory of oil). Since you are clearly versed in this subject, my question is what happens if we actually do use up all the oil? Is it even possible to produce the energy the world requires even at current levels (disallowing for growth) without oil, from ANY source? I would guess nuclear power would work, but it's not portable / storable like petroleum energy is.

Well thats the problem isn't it. Nuclear power isn't the solution to the oil problem because it isn't competing with oil. Nuclear power is competing with coal which is already much cheaper than oil. It is a real pain to be able to take energy that is so easy to move around on the electrical grid and put it into an automobile. If it was easy, we'd have electrically powered cars running from coal electrical power plants.

Hydrogen, batteries, and fuel cells need a little discussing here. Hydrogen isn't used in pure form because unless you use cryogenics or very high pressure fuel tanks the energy density will be much too low for long trips. Neither of those options is going to sell very well. Batteries are only now approaching the point where they may be feasibly used for short trips in a city (ideas like the plug-in Prius modifications are brilliant). So this is certainly an advance, but it doesn't help for longer trips (i.e. trucks). And fuel cells require either high temperature fuel cells that take hours to warm up or low temperature fuel cells with expensive catalysts. And even those fuel cells will need to get their hydrogen from reforming a hydrocarbon to achieve a decent range (i.e. a gas tank).

So in the short term we are stuck with oil. It is my hope that ultracapacitor and battery advances in the future may make it possible to cut out hydrocarbons from trips of less than 50 miles or so. And hopefully fuel cells will become economical. They will be extremely beneficial because they operate with much higher efficiencies than other hydrocarbon engines.