If you can measure AC voltage, you can easily measure AC current as well. Just place a relatively low value resistor inline with the load, and measure the voltage between each leg of the resistor. Then divide that voltage by the resistance to get current. You can then multiply that by voltage again to get wattage.
For example, if you used a 1-ohm resistor and measured 0.5 volts across it, 0.5v/1=0.5A. Thus, 0.5A X 120v = 60W. Ohms law.
If you don't have a resistor handy, perhaps you can measure the resistance of an extension cord with your multi-meter and use that instead of an actual resistor. Remember to test the resistance of shorting the leads of the meter and subtract that from the measurement of the extension cord to get a more accurate resistance reading.