how to determine the wattage of a stereo?

Wattage doesn't increase as your volume increases. The voltage output across your speaker ports are increased (in most cases, anyways).
Stereo wattage is based on the amount of wattage the speaker outputs can produce.
Using Ohms Law, V=IR and P=IV, you can see that resistance plays an important part. With a constant voltage, as your impedance lowers, your amps increase. They're indirectly proportional. So, when your speaker ports are rated for 8ohms, you cannot hook up speakers that are less than 8ohms, otherwise, you'll pull too much current from your ports and run the risk of blowing your stereo.

To answer your first question, you can read the label on your stereo near the power cord. It usually lists the voltage and input amp values. Multiply the two, and you end up with the wattage that the stereo pulls from the outlet on the wall.
 
In the Back (or bottom), it should have a little label with Voltage and Power or Voltage and Amps requirements. Ex. 110 V, 5A (that is 550 W) or 240V 500 W; Otherwise you need an amp meter to measure how many amps it draws.
 
Basically a stereo today is a 6 channel surround sound. The normal watts for a Sony for instance is 100. The volume control will increase the wattage to the speakers but the maximum watts of any stereo system will destroy the speakers! The Ohms of speakers must match the maximum wattage of a stereo system be it basic 2 speaker or 7.1 system surround sound system. Usually the speakers that come with a surround sound system are compatible. If you for instance have an old Radio Shack stereo Amplifier and want to hook up some 15 inch musical instrument speakers then you will probably have no problem. But to hook up little speakers to a powerful amplifier can spell disaster.
 
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