[kazga]

Not true. You can't really train your muscles to use less oxygen for the same energy output (what "oxygen-efficiency" would imply). You rather increase their capacity to take up oxygen from the blood and burn it. They will use more oxygen to output more energy.

That additional oxygen needs to come from somewhere. Endurance training at the same time trains the heart to deliver more oxygen to the periphery; the primary mechanism is increased cardiac stroke volume.

[bluGill]

You kind of can - the muscles can use aerobic or anaerobic processes. When you develop brute strength you are training those anaerobic processes. That isn't what OP was talking about, and overall it is much less energy efficient, but it does produce a large burst of energy when needed and you can train your muscles that way.

[gf000]

I would assume that another factor is that the technique for a given exercise on the other hand can be improved, and that can help with decreasing the necessary energy - would that be a correct statement? And as a follow up, depending on activity type this may or may not be significant?

[frocodillo]

Yes, definitely. Technique is partly about efficient mechanical movement, sending the various parts of your body in the right direction(s) and not waste effort on movement that doesn’t contribute to propelling you forwards. But for endurance sports, it’s really about minimizing energy cost at a given speed. To use running as an example, you can improve biomechanical efficiency through better timing, correct loading of tendons, tendon stiffness, elastic energy use, and more.