HI!
This is how I see it. Someone to confirm?
The output power of a transformer depends on the Current drawn from it and the Voltage developped across it. Then, you just take their product (and you might divide by square root of 2 to get RMS values). The result would be the power of the winding, in VA.
The gauge of the wire, again, depends on the current drawn from that winding. At 2000W, the current could be 1A and the voltage will be 2000V, or the current could be 100A and the voltage 20V. In the first case, the wire shouldn't be as thick as in the second case. So, to determine the gauge, please specify the current.
About the number of windings, I'm not sure but I think that you should look into power transfer. Say, your transformer has 70% efficiency. Then, the output power will be 30% less than the input power (if input is 100Watt, the output will be 70Watt).
Also, the voltages depend through the ratio of number of windigs. If you put 10V on the primary with 10 windings and you take the output at the secondary with 100 windings, the output voltage will be 1V. The current will be bigger though. The formula is: n1V1 = n2V2, where V is voltage, n is the number of windings and numbers 1 and 2 are the primary and the secondary windings of the transformer.
With all that in mind, you should be able to figure out the number of windings and the thickness of the wire (there are tables on the internet that tell you the AWG of the wire for a particular current. Google for them).
Example:
output power needed 70Watt, then the input power will have to be 100Watt (70% efficiency).
input voltage: 100 Volts
output voltage: 10 Volts
So, the ratio of windings will be: for every winding of the secondary, there will be 10 windings on the primary.
Now, the input power is 100Watt, with 100Volts across it. So, there will be 1Amp flowing through the primary.
The output power is 70Watt, with 10Volts across it. So, there will be 7Amps flowing through it.
So, the secondary will have a thicker wire than the primary (more current flows through the secondary). Going to:
**broken link removed**
in Table 2, we can see that for 1Amp, wire should have AWG of 20 and for 7Amps, AWG of 14.
Hope this helps,
TI|CP