Oil is not a likely power source; it would burn too hot, and the power plant would be too large. The oil is most likely a lubricant for the huge number of finely-crafted joints a machine would require to mimic human motion. An oil change is probably a weekly occurance (meaning Dorothy probably goes to the bathroom once a week).
This problem extends to the Megadeus level, too. There is simply not enough room in Big O for the power systems required. A nuclear reactor would be almost as large as Big O itself (unless the designer didn't mind their Dominus having radiation sickness), and still wouldn't have the energy reuired to run the systems.
I have guessed that Dorothy has a bio-converter, allowing her to use energy from food (and allowing her to eat), but even that wouldn't allow her to perform at her observed superhuman levels unless she ate more than a human (even if she got all the energy out of the food, as opposed to a human's 25% or so). The converter would be for appearance and as emergency power.
I would surmise that the power core for an android or Megadeus is something REAL ultra-tech, something we can only theorize about. It isn't a battery, since it never needs replacing or recharging. Since so much of Dorothy's innards would be her solid skeleton and the bio-converter system, she would need something compact. We might label it a zero-point generator or something, but that would be a guess. Why not just call it a "power-core" or "heart"?
A Megadeus would have the same system, probably more compact or decentralized. As well as the fact that Big O has even less internal space than Dorothy, what with missiles and plasma projectors and garages and that Final Stage cannon and the room for the chains. So perhaps it has a hundred or so Dorothy-type power-cores scattered throughout it's body, so such a vital system couldn't be targeted by an enemy.
Actually, that raises another question; WHAT THE HELL IS INSIDE THAT MEGADEUS??
The chains on Big O's harpoons have been shown (in the battle with the three Megadei) to be over two miles long each; a dozen of them all coiled up would fill all of Big O's volume! And where is the ammunition stored for the arm-gatlings? Surely not inside the pistons, since such storage bays would weaken the pistons and make them shatter in use. And the missile bays were shown to cover all of Big O's torso - whence then came the plasma sphere generators, the Final Stage cannon, not to mention the elevator that carries Roger from the foot-garage to the cockpit? And as for that foot garage - how the devil does it not crumple like an accordion when Big O walks??
For that, I can come up with only two theories. 1: Big O accesses multi-dimensional space, rotating the equipment into 'real-space' as it is required. 2: Big O's innards are a seething mass of pre-programmed nano-technology, which shapes itself into what is needed. Of course, booth of those theories have flaws.
I think I've done enough damage here.
