...determining the impedance of a random output transformer.
I can help with this one.
All you need is a DMM that can measure AC, and a source of low-voltage AC with a frequency within the range of the output transformer. An audio signal generator set to, say, 500 Hz is ideal, but if you don't have one, you can, in a pinch, use a 6.3V AC heater winding as your AC source. (This might be a little inaccurate because cheap guitar OTs may not work properly at 60 Hz, but it will at least get you close.)
If you pulled the OT out of a piece of equipment, you already know which wires connect to the primary winding, and which ones to the secondary. If you got the OT sight unseen, set your DMM to measure resistance, and measure away. The secondary winding will have a very low DC resistance (probably well under one ohm). The primary winding will have much higher resistance, typically many tens of ohms, maybe some hundreds of ohms if it's a small and cheap OT. If there's a centre-tap on the primary, you can identify it because you'll get (very) roughly half the resistance between this point and each of the two ends of the primary winding. (Usually the transformer manufacturer is also kind enough to physically position the centre-tap in between the other two wires, but this isn't guaranteed.)
With the primary and secondary identified, connect an 8 ohm resistor across the secondary winding. (Use 16 ohms if you know for sure this transformer was designed for 16 ohms, and 4 ohms if you know for sure it's a 4 ohm transformer.) The resistor doesn't have to be exact - if you can't find 8 ohms, use 8.2 ohms. Similarly, you can use 3.9 ohms instead of 4, or 15 instead of 16. The resistor also won't have any significant power delivered to it, so you can safely use a quarter-watt or half-watt one.
Now connect your AC signal to the
primary of the output transformer (not the secondary: this will cause dangerously high voltages to appear at the primary, which we do NOT want.) Use your DMM to measure the voltage across the primary, and across the secondary. Write down both voltages. That's it, you're done. All we need to do now is a little basic math, using the two voltages you just measured.
As an example, let's say your DMM measured 6.252 volts AC across the primary, and 198 mV (same as 0.198V) across the secondary.
Calculate the voltage ratio, which is the same as the winding ratio (number of turns in the primary winding / number of turns in the secondary winding) inside the transformer. In our example, the voltage ratio is (6.252/0.198), which calculates to 31.6. (I've rounded to 3 digits, because we only have 3 good digits in our secondary voltage measurement of 198 mV.)
Transformer theory says that the impedance ratio is the square of the voltage ratio. So let's square 31.6, which gives us 998.56, which rounds to 999 (rounding to three digits again.)
This means that if you had a 1-ohm speaker, the transformer primary impedance would be 999 ohms. If you had a 2 ohm speaker, the transformer primary impedance would be 2 x 999, or 1998 ohms (basically, 2 kilo ohms.) Obviously, if you had an 8 ohm speaker, the transformer primary impedance would be 8 x 999, or 7992 ohms...what you've got is an 8 kilo ohm OT primary.
And there you are, you've just magically figured out your OT primary impedance! Congratulations!

-Gnobuddy