Looks like something is very badly miswired.
To have even a chance of figuring this out, we will need to know what wires go where (how many cables in each box, which color goes where). Also, if you could do the measurements with a load on the circuit (measure the voltage across a pigtail lampholder) and with the other bulbs removed, so we can eliminate any phantom voltages.
We already know that light one has problems - even if the neutral is switched there shouldn't be any voltage on the white wire unless we are seeing voltage thru the other bulb and they are in series. Voltage on the ground wire is even worse.
I agree with calling in an electrician on this one. It sounds like there are too many problems, not only on this circuit, that should be fixed for safety reasons.
/mike
