Here is my limited understanding. I'm sure someone will correct me if I'm wrong. If this is stuff that you already know, just ignore me.
What you are measuring when you measure a diode is the forward voltage drop, in volts, from anode to cathode. The cathode is usually the end with the stripe (except on some Russian germanium diodes I have!). So you have one diode with a forward voltage drop that is 0.26 volts and another that is 0.32 volts.
The forward voltage drop is kind of a threshold. If the voltage being passed to the anode of the diode is below the forward voltage drop, the diode will not conduct and nothing will pass out the cathode. When the voltage at the anode exceeds the forward voltage drop, voltage will pass out the cathode of the diode. The voltage you measure on the cathode side of the diode will be equal to the voltage on the anode minus the forward voltage drop of the diode.
Now, how this impacts an audio circuit is where my knowledge becomes a bit fuzzy, but I think I'm pretty close.
Let's say you put a couple of diodes with a 0.3v forward voltage, anti-parallel from signal to ground. If the signal is below 0.3v, the diode does nothing. The forward voltage drop prevents any signal from being passed to ground, and the full signal is passed on to the next point in the circuit. When the signal rises above 0.3v, the diodes conduct. This causes any signal above 0.3v to be passed to ground, only allowing the first 0.3v to pass to the next point in the circuit. The process of passing anything above the threshold to ground literally clips the top and bottom of the waveform off so it is flat(ish). This clipping makes the signal distorted.
You can use different diodes to get different cutoff voltages. Germanium diodes are around 0.3v, silicon around 0.7v, LEDs from 1.6v (or so) on up. Using different diodes in a clipping arrangement can yield different distortion characteristics.
That's just one way to use a diode. I'm sure there are many others.
I hope that helps.
Mike