I dont know if this applies to you totally.
Primary oveloading can occur in 2 main ways, too high a current per mm2 of copper, this can be checked by measuring the current into the primary and measuring the physical size of the copper, core saturation isthe other, this can be checked using a 'scope and a resitor in series with the primary, distorion of the current wave indicates saturation.
Oveloading the secondary on a well designed transformer can usually be found just meassuring the voltage and calculating it back from the transformers regulation parameter, and of course by observing how warm the trans gets.
You can al;so measure he phase difference between the pri and sec, but you need comprehensive data on the transformer to know what to expect.
This is only a rough guide (before someone smokes me).