In any case, you need to measure the voltage on the speakers or headphones. This may require DIY cables or connectors, if you do not have a connector (like the splitter recommended for headphones) that makes it possible to access the terminals with a multimeter.
Not necessarily if at least one of your speaker amplifiers or receivers has a balance control. Then you can adjust it to match the imbalance of the other device. Another solution that may work is to use different volume settings where the difference is smaller, and change the source volume as well to compensate. With devices that do not use potentiometers, there might not be much imbalance to begin with. It also may not be necessary to match the channel balance as accurately as the overall levels (which can be calculated as the square root of the sum of the squared left and right voltages), but I am not sure what the maximum acceptable amount of error is.