If the charger's output current and voltage are the same when it's charging as when it's doing power supply work, then it's consuming the same amount of input power; it couldn't even tell the difference between the two.
If the output voltage is higher, then the power is of course greater...and conversely if the system voltage is lower, the output power is lower, assuming the current remains constant. For a typical current limiting power supply (as opposed to a constant voltage-constant current supply which regulates the maximum current), the transition into current limiting isn't super precise and the voltage may sag as the current limit is approached.
In the generator, the engine speed and throttle are adjusted by the generator's brain based on the load, which varies the voltage and current output of the internal alternator. (I would assume it's also adjusting the excitation voltage at the same time, though I would be clueless as to the exact relations between RPM and excitation voltage it maintains as power consumption varies). Since the output you see is synthesized and not directly from this alternator, the fluctuating voltage is of little import unless it drops too low due to overloading or a sudden large increase in power consumption that the engine isn't quick enough to respond to.
I rather doubt you'd see significant gains in power from "better" gas or synthetic oil. If the carburetor or air filter needs cleaning or the spark plug is worn or the valves need adjusting, fixing those could very well improve the power output. My guess (and it's only a guess, not even a hunch) is that you're simply consuming more power now, not that the generator has degraded performance compared to previously.
