What takes oil leaking from car engine off a paved driveway?

Take a look under the hood in the dark .You will see if it shorting out by the blue flashes I think oil leaking is the problem Also the oil breathing dystem may be blocked.

I always buy a service manual from advance or some parts supplier for every vehicle I own, that way the manual tells me how the parts are mounted to the motor and their location to the rest of the motor.
I am not sure where the starter is located on a Pontiac G6 but look above it if you have to use a flashlight, if your oil filter is near it, make sure it is tight and not loose.
Sometimes valve pan gaskets leak and run down the side of motor making us believe oil is coming from another place, just start looking and you will find it.

Take it back to the oil change place. Or check the oil. If a seal is leaking or oil filter was not tightened or put on correctly oil may have leaked out and you will blow your engine!

Is is there any oil leaking in garage or driveway or where you park?

could be from a number of places have the engine thoroughly cleaned and then look for fresh oil drips starting at highest point of engine working way down

This car has a catalytic converter, you can't see the smoke of the burned oil with it, it's cleaned. The oil could get in the plugs cavity only if there's a leak at the valve cover. My guess is that the oil seeps out only when there's pressure - the engine is running. To find where it leaks clean your engine thoroughly the start the engine in your driveway for an hour - where the oil will leak you clearly see it. In that case replace the corresponding seal.

Common oil leaking areas on that engine is the plastic lid on the oil filter,and the gasket in between the oil filter adapter and the engine block.I would suggest you take it to a qualified shop and have them diagnose the oil leak.

Try changing oil brands. If you want some good info on oil burnoff rates etc google noac volatility tests.I could explain it here but it would take an hour.
Good luck!

Could be some thing as simple as a leaking filter, drain plug, or oil pressure sending unit. If it hasn't been in for an oil change lately, take it in, mention you have seen drops on the driveway, the tech will likely note the leak and possible solution. From this you can determine the cause and cost.

Doesn't sound serious yet. Take a good look for oil pan leaks, valve cover gasket leaks, oil filter, etc. just to know what it is. You may be able to get a clue from where the drops are.

likely either the steering rack&pinion assembly is leaking or the hoses to it are leaking, have it put on a lift to see which steering componet the fluid is leaking from.