How is the lighting panel of an Airbus A340 designed and how does it work?
Nav and logo.

The logo light is a spotlight which illuminates the tail to show the airlines logo at night.  The Airbus A340 has two circuits for NAV/LOGO. Logo is an auto option when the landing gear is not compressed or the flaps are extended at 15º or more." in both positions, 1 and 2.

Dome is the cockpit ambient lighting.

Strobe on means the strobe is lit.  Auto means that the strobe is on when the landing gear is not compressed - i.e. it comes on just at the point of take-off and switches off on landing.  The point of having "on" as well is that some procedures require the strobe to be turned on just before entering the active runway and when leaving it.

Hope this helps.

Picture of the panel: