Ground wire behaves weird
Best guess from the limited details is that you have a ground/neutral short somewhere and also a switched neutral. That would result in the lights always being hot and turning on as soon as there's a path to neutral or ground.

To diagnose this, you'll need a voltage tester that can handle line voltage (120vac). White to ground should read near 0v, white to hot should read 120v, and ground to hot should read 120v. Then disconnect the line from the load and check for continuity in the circuit. The switch should show no continuity when off, and near 0 ohms when on. And the ground should show no continuity from both the hot and neutral wiring. The neutral to hot should show continuity until the lights are removed from the sockets, at which point it should show no continuity.

If the voltage readings indicate a reversed hot/neutral, then correct them and label the issue so it doesn't confuse a future electrician. If the continuity tests show unusual readings, there's likely a short and I'd recommend disconnecting the light fixtures and retesting after connecting them back one by one until you locate the short.

Standard disclaimer: if you're at all uncomfortable around household voltage or do not know the proper safety precautions, please consider hiring a professional electrician.