All of this "soaking with oil" will only make the fibers swell and tighten the plug.
Find a piece of steel (brass would be better) rod that is smaller than bore diameter, chamfer the sharp edge, and drive the stuck snake out from the other end. Use light taps with a very small hammer.
The long wood screw trick might work, too.
Don't use oil, don't use chemicals. If these methods don't work, take the gun to a good gunsmith.