What device measures an electrical generator's output in units of energy (watt/hours, joules)?

There are numerous ways to measure a generator depending on what you are wanting to measure. To start off there is a very important formula Watts = Voltage x Amperage

With this formula, we can design an array of generation and distribution of power safely.

Generators are classified by kwh or kilowatts per hour. A normal size generator from Homedepot 5-10kw. (Thats 5,000 watts per hour) A hotel or office building will have a large generator in the area of 60-80kw (60,000watts)

Watts is "power" in the sense of labor or force.146 watts = 1 hp roughly

Voltage is defined by the difference in potential energy between two points. Ie, a generator lead and the ground plug.

And finally Amperage is defined by the # of electrons going past a given point per second. 1 amp = 62,400,000,000,000,000 electrons (This a VERY watered down definition of an amp)

To sum this all up, you can use a volt meter to measure voltage, an amp meter to measure ampers and with these two, you can find watts.

120 volts x 1 amp = 120 watts

A watt-hour meter measures a generator's output

electric meter,energy meter all so seen them listed by "watt hour meter"

If you mean how many watts are being used at the time it was being tested that would be a normal voltage meter.