In the game series Deus Ex, they describe something called bioenergy. Energy required to power augments is stored inside internal 'batteries' that can be drained over time or with heavy augment use. You can read more about how augmentations developed and how they function in the games here.
For the purpose of your story, the scientists of your future would have to have figured out how to engineer synthetic muscle fibres and nanites that could power the fibres through the usual ATP cycle that our bodies already use. If these were efficient enough, then even if the limbs didnt look natural, they'd function the same as normal human limbs.
I wonder though if these nanites would be able to produce enough energy for an artificial limb to outperform human strength, that will depend on your story I suspect. The robotics to provide the same range of motion as a natural limb would be insane, but feasible I think (since the nanites could build the smaller parts).
You could also, like Deus Ex, have several generations and manufacturers of the limbs - thus giving different characters different levels of augmentation. Some better than others.
Realised I should also mention that muscle cells fire using an ATP sodium-potassium ion pump. You can imagine each cell acting as a kind of battery. A muscle contraction activates that battery and it discharges. Biochemical actions restore the cells energy but over time there is fatigue (through further complex biochemical processes). The nanites would need to fill the role of the muscle cells and potentially even be able to differentiate to fill the roles of other cells in the body (red blood cells to carry oxygen and carbon dioxide, white blood cells to fight off infections and repair damage, platelets to seal wounds, etc).
To answer your question about glucose, the overall process of oxidizing glucose to carbon dioxide (burning) is known as cellular respiration and can produce about 30 molecules of ATP from a single molecule of glucose. The ATP cycle is how energy is produced in the body, except that glucose isn't necessarily the only source.
Electricity is essentially the flow of electrons, the energy released through cellular respiration is primarily heat I believe (that's why you get hot when you exercise). I can't see how that process would generate electron flow.