Transformer Size?

If you are able to apply voltages and watch current with an oscilloscope, you can see where saturation sets in . The nominal voltages would be just a little below this.

The secondary voltage will be the result of applying a primary voltage. Measuring the resistance can give you a rough idea of the turns ratio (the relationship between primary and secondary), but having said that the transformer's behaviour will also be affected by characteristics of the input, including magnitude, frequency and harmonics.