It looks like a steel frame bike, but is the headset lock ring steel or aluminum? If steel then you need Liquid Wrench not oil. If it's aluminum then pour some ammonia on it instead-but don't breath this stuff!
Because aluminum expands with corrosion, you cannot loosen a frozen stem by force, so be careful applying force because many forks have been damaged by forcefully attempting to free the lock. Don't do it. If all else fails ask a skilled mechanic to grind it until it breaks through one side of the shell to extract the ring.
If the lock ring is steel, then allow a liberal amount of Liquid Wrench to penetrate overnight, then reapply then just try to wiggle it.