Troubleshooting: Why does my multimeter not work when a non-contact volt detector shows current?
At the switch it sounds like your "ground" is not actually connected to the grounding system. 

At the light fitting it sounds like your neutral wire is not actually connected to the neutral.

What makes this situation really worrying is that the combination of results on the light and the switch strongly suggests to me that a "bootleg ground" and/or "bootleg neutral" is involved where a Neutral is used as a Ground and/or a ground is used as a neutral. If this was the case then you may well find that when the switch is on and a bulb is in the light that the switch plate is live.