Unless you can get to the backside of the O2 sensor remnant, so you can wet the threads from the inside of the pipe, penetrating oil is a total waste of your time.
The threads are sealed with a gasket, exactly like old-style gasketed spark plugs. The seal is air-tight. Penetrating oil cannot get into the threads to do any good until you've already backed the sensor out a half-turn or so. By then, you don't really need the penetrating oil. The penetrant does make a lovely puddle on your driveway, though.
If your manifold isn't bolted to the head air-tight, you'll get leakage out...and air leakage in. This can screw-up the O2 sensor signal, leading to false "lean" readings; and then the computer adds more fuel to compensate.
Make plans to remove the manifold, and remove the broken bolts. Get the manifold planed if it's to be re-used, or find a replacement. Any way you look at this, the exhaust system needs to be sealed-up AT LEAST to the catalytic converter, and ideally to the end of the tailpipe.