POWER SUPPLY TRANSFORMERS
When testing transformers use an ohmmeter to check for continuity and the absence of direct shorts.
Primaries windings measure from 2 ohms to around 20 ohms on most hi-fi amps, and the secondary windings for the high voltage will usually read between 40 and 200 ohms. Filament or heater windings operate at lower voltages and they will typically measure 1-ohm or less.
Using a Variac, remove all the tubes and test each winding with about 20 volts AC to the primary windings. You should have about 1/6th of the rated voltage AC at each winding. About 1 volt on the 5 and 6-volt windings, and around 40 - 80 volts on the high voltage windings (your results may vary depending on the actual rating of the transformer).
A power transformer that is leaking tar or oil is not necessarily bad. But, it has been over-stressed at some point in its life.
This is a good visual sign that something else has gone south in the amp. You should do further troubleshooting for an over-current condition in the amp (looking for a possible leaky coupling capacitor, shorted power supply capacitor, improper bias setting, etc.)
These special transformers are designed to couple the high impedance output tubes to the low impedance voice coil of the speaker. The most common killers of these transformers are high current conditions caused by a shorted tube, a unstable resistor, a defective bias circuit or improperly adjusted bias, or shorted coupling capacitors.
You can use an ohmmeter to check output transformers for continuity, as detailed above. You should see roughly 200-ohms between the B+ center tap terminal and either connection from the output tube. You can also measure the output windings, with no speakers connected. In general, the resistance between the ground or common tap and the 16-ohm tap will about 1-ohm. Figure on about .50-ohms for the 4-ohm tap. Split the difference (.75-ohms) for the 8-ohm tap.
It is imperative that your tubes be in reasonably good shape, and that you bias the amp in such a way that it does not exceed the power rating of the output transformer or the plate dissipation rating of the output tubes. Amps are needlessly damaged because their owners do not take the above precautions.
Replacement transformers are nearly impossible to find at any price. Any time you see an output tube plate glow red TURN THE AMP OFF IMMEDIATELY! Determine why this condition exists. Failure to do so could cost you a transformer or two, or essentially the heart of your amp.