Fred, it's been so long since running into one of these, I'd almost forgotten about them, but it sounds like you have a low voltage relay lighting system. These multiple green, white, and black wires to your switch...are they relatively small, such as thermostat or bell wire would be? Another clue is that often with these systems when you'd switch on a room light, you would hear a "click" not from the switch, but from an indescript point somewhere above the ceiling; this is the relay control box that was often placed in the attic.
Most done in the late 50's & early 60's, these weren't very common (the idea never took off), but basically what this amounts to is low voltage wiring & wall switching, which all routes to one central relay box that then switches the 110v for your home's lighting.
Conventional switches/dimmers will not work with this system, and you are left to either find a source for replacement switches, or have the switching rewired in the conventional manner & bypass the relay box.