How many Watts is my stereo?
The specification says it consumes 320 watts. 


I would go with that as a first estimate and, assuming that is a Class A-B type, that the efficiency is about 50 to 60% at maximum volume and so the audio output is about 160 W.


  It also says the continuous power output is 100 W per channel. 


You can't get 600 W out for 320 W in so someone is stretching things. Each amplifier may be capable of 100 W but the PSU won't be.


  It also says the RMS power output is 144 W per channel. 


RMS isn't applicable to a power measurement. RMS stands for root mean squared and is related to the heating power of a waveform. Since \$ P \propto V^2 \$ or \$ P \propto I^2 \$ the squaring has already been done. Power rating should be quoted as the peak power or the average power for a particular test signal - sinewave or a particular piece of music.


  When I advertise this thing, how many watts can I call it? 320 watts? 600 watts? 864 watts?


I would recommend that you say something to the effect, "Fills an 8 m x 5 m room with dance party level music with good bass and without distortion."