Electrical issues

Dodge is running for the first time in years.

Infact it's running so well it no longer turns off on the key

Have to smother carb intake in order to kill it.

Any ideas? Before I start looking into it. I'm thinking maybe the ignition switch.

When you connect a battery terminal the 'oil' light comes on on the dash as if the ignition is switched to on. But without a key in the ignition.

Then flick key to on position and oil light flickers a little but stays on. Then flick to start and it fires up. Switch it back off and take key out does nothing.

On a side note wipers and indicators no longer work either, don't know if related or separate. Main lights work fine.

Disconnect your battery when you are not intending to start the car, because you have something in your ignition circuit wiring connected direct to 12v.
This is why your oil light comes on when the battery is connected, and also why it won't shut off.

Just for kicks disconnect the alternator field wires when the keys is off and see if the motor shuts off.
If it does this will narrow down where the problem is substantially.
Also, when you want it to shut off, disconnecting the battery should shut it down instead of flooding the motor and washing down the cylinders of oil.