How to calculate the efficiency of a sinewave inverter?

I may not understand your question completely, but it doesn't appear that you've given enough information to calculate efficiency (which is usually considered to be a ratio of actual to theoretical yield).  If you have a 180 amp-hr battery, you've specified the amount of ENERGY the battery holds (once you know the battery Voltage).  If you have an inverter rated at 800VA, you've specified the amount of POWER the inverter can deliver.  These two are related by time (Power = Energy / Time).

As an example, suppose you have this battery which provides power to the inverter at a voltage that the inverter can convert from effectively (e.g. 12V).  If the battery delivers all it's power at the rated output voltage (or at least at a voltage high enough for the inverter to operate, let's assume 12V for this example), AND the inverter is delivering power at its maximum capacity of 800VA, then you would expect that the combination could drive whatever load was connected for a period of time:

Time = Energy / Power  = [180 A*hr*(12V)] / 800 V*A
   = about 2hrs 42min

To calculate efficiency, you'd have to know something about how much power was lost in the inversion process.