The Sony MDR-V6 headphones has a sensitivity of 106db
and an impedance of 56 ohms.
Other headphones usually are in the range of 90-100 db
but lower impedance.
I read somewhere that the higher impedance, the higher
output from a standard 8 mW HI-MD minidisc player?
How is the sensitivity compared to the impedance have
an impact of the power output from the amplifier?

You've got it backwards. Typically the lower impedance the higher the power output will be. Theoretically for half the impedance, you double in power. However many amps are regulated so the power doesn't always increase by 2 when you halve the impedance.

Note, however, that when you use lower impedances you also put more stress on the amp. This introduces more noise and distortion to the signal.

Sensitivity is another story. Sensitivity is not necessarily related to impedance but it may be something to take note of. For one set of 'phones with a low sensitivity compared to another set of 'phones but having a lower impedance probably makes up for the lower sensitivity since it draws more power from the amp.

In this particular case, you have a high sensitivity and a relatively high impedance. (Headphones are usually 16-32 ohms, right?) So despite the fact that you're probably drawing less power from the headphones amp, you're still getting good ouput per mW so the volume again probably won't be affected. Plus with the higher impedance, theoretically, the lower stress on the amp will produce better S/N and lower noise/distortion.