If you have a regular $3 multimeter, it should be able to measure current and voltage between the battery and inverter. Then just multiply. double check you're on the right mode and using the right socket on the meter before connecting, or you'll get a big bang!.

For the AC side, it's much harder to measure - typical inverters have rather imperfect AC outputs, and unless you have a rather expensive multimeter you won't get an accurate power measurement. A kill-o-watt will probably be okay for a rough measurement, but there might well be a +- 20% error...