You don't actually need to use a signal generator - since this is a mains transformer, you can use a low voltage (maybe 6-10V) transformer as your source. Whichever you use, measure the ratios of the windings. If there are multiple taps on a coil, see if any of them are centered. Watch for coils that give the same output voltage as you're feeding in. Now play 'what if'. i.e. If I connected mains voltage to this coil, what would the voltage be on the other coils & taps? See which combinations give you some rational results. Be careful when you make these measurements. If you put 6V into a low-voltage winding, you'll have line voltage at the primary windings!
Five wires on one coil suggests a multi-tap secondary with a center tap. Image two bipolar supplies with full wave rectification and a grounded center tap. The higher voltage pair is for the output drivers and the lower voltage pair is for the low-level circuits. You might see this in a high-power audio amp.
On the primary side, the 'magic' voltage ranges are 220 - 240V, 110 - 120V, and 90 - 110V. The last range is for Japan where the nominal voltage is often 100V. I've seen transformers where only one of the two primary coils has a tap for 100V.
Once you've figured out the primary and secondaries, look in a catalog and find a toroidal transformer that's about the same size and weight as the one you've got. Ideally you want to know the dimensions of the core, but that's often hard to measure because it's hidden under the windings. That will give you an idea of the total power you can draw.
If you have more than one output winding, determining the rating of each coil can be tricky. One source I saw suggested that a 10% drop from the no-load voltage was reasonable. Smaller transformers allow a larger drop, while for larger transformers, 10% might be too much.
It's not an exact science, but transformers are pretty rugged so a bit of overload here or there shouldn't cause any problems. Remember that a fully-loaded power transformer will likely heat up to the point that you definitely don't want to put your hand on it!
Ed