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The current is limited by several factors that occur at different currents.
1. Heating
2. load regulation ( usually the series resistance drops 2% to 5% of the voltage this includes both primary and secondary resistance drop.)
3. core saturation
Usually the weight of the transformer is a good clue. Compare it to others by the same manufacturer to get the power level.
most transformers are made of standard (or nearly standard) cores. For each core there exist a max power value. You can divide this value by your output voltage and you receive the max. output current. Pay attention if you have more than one output!
If you have a variable load available you can check when the transformer starts to get hot !! Not precise at all but if you go slow you can use it in a safe region....
The short circuit test above will allow you to meassure the turns ratio with a clamp on current meter. It will also allow you to measure the leakage inductance (which is very small in a power transformer)
What I expect is that if you put a low voltage on the open turns the heat generated in the losses will raise the temperature which can be a factor in the power rating. However, you have to know the rated external temperature to tell when you reach the current limit.
The post above about the weight and size being the best indicators is probably as good as you can get without looking at the catalogs for the part number on the unit.
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