Answered this a few days ago with links on the owner's forum, but will add info here for those not in that forum.
The original iPhone charges fine and works fine with the JVC (in aux mode, not changer mode - the link in the previous reply shows how to change it).
The 3G iPhone works fine, but does not charge with the JVC, but I bought and am using the CableJive charging adaptor (<$20) another owner suggested, and it works great.
I have not tried the newest nano, but assume (with all the dangers inherent in assumptions

) that it is, like the 3G iPhone, no longer capable of charging from the firewire based pins, and therefore needs a charger adapter too in order to charge, but should work as an audio source already.