How to determine which camera batteries will take the most photographs?
You will need a constant current load. To find out the current required, connect the camera to the battery via the multimeter and record the current draw while it is taking a photo in burst mode. Now make a constant current circuit for that current (not a trivial task, but not too difficult either). Fully recharge each battery and then discharge it through the load to find the time it takes to go down to 3.7V or so. That is the time available for active shooting. There will also be a time for when the camera is on but not taking photos, where the current draw will be less. Make sure not to discharge the battery too quickly, or too much.

Some more expensive battery chargers might also have a discharge function which will tell the mAH capacity of each battery. They may also have an option to set the discharge current. This is probably the easiest method.

The term is energy capacity. Energy is power x time. Power is measured in Watts, energy measured in Watt hour. Watt = Volt x Ampere. Battery capacity is measured in Ampere hour. Li-ion batteries have a nominal voltage of 3.7V (and you probably don't want to discharge them below 3.6V regularly). So battery energy is 3.7 x mAH. You can measure mA with the multimeter, but you need a load drawing a fixed mA to find the hours. mAH is printed on the battery, but that may not be reliable, and varies with current (mA) draw.