Hi there,
Well, some of those coils can be checked with the output of the function generator such as the XR2206 chip, but others will require some higher current levels to really test the inductance. The metal core ones most likely will need some higher current levels to get the flux up high enough on the BH curve to get to the part with the normal operating permeability. Not doing that could lead to a quite incorrect measurement of the inductance.
Also, a coil used for a switching power supply is probably best tested in a circuit that actually acts as a power supply. That way you can tell what the inductance is by looking at the waveforms and also how it reacts to higher level DC currents, which is something you'd want to know as well as the inductance. You'd want to know at what level the DC current starts to degrade the inductance. You can get some idea by looking at the lead wire gauge so that might help too.
To test it outside of an actual power supply you have to get some DC current flowing and see how it reacts. You might build yourself a little test jig which is actually a buck converter, where you have some decent level of power coming in and going out, and can look at the current through and voltage across the coil. To find out what a buck circuit looks like you can look on the web im sure there are plenty of examples, but if not i'll post a schematic.
To test the little coils you can use the frequency generator and maybe a series resistor where you can check for the response of the coil with frequency. That will tell you the inductance. To use it with the bigger coils, you'd have to use an amplifier or maybe just a transistor and power supply to pump the coil with a square wave. Measuring the response of the coil to a square wave can tell you the inductance, and you can set the DC current if you use an external resistance and vary the level of the wave (using a square wave that is positive only, not plus and minus, and this kind is quite easy to generate).
So to start maybe you can build a little buck converter. It doesnt have to be regulated so it's going to be quite a simple as all heck circuit. Just a transistor or two or three for the drive, a back 'catch' high speed diode, maybe a 555 ic to provide the frequency wave, some load resistance, and a power supply that can handle the current you need to test at. This is really the simplest way to go about this and you'll see how easy it is once you do a couple chokes this way.