Sounds like you are reading the resultant voltage of Capacitive Coupling (if you are reading L-G and getting the wierd readings as stated).
Make sure the Common Grounded Conductor (AKA "neutral") is connected properly between source and load(s).
Also make sure the Equipment Grounding Conductor is connected properly between source and load(s).
Sounds like you have both - an open Noodle and an open Eq. Grounding Conductor, only the EGC is physically connected to earth ground somewhere, but not connected to the source's Grounded Conductor.
Let us know the outcome!