Oil in the water stems from a crack in the block between the oil galley and the coolant jacket.
When the engine is running the oil pressure > coolant pressure ,so the oil flows into the coolant jacket.
When the engine is stopped, the oil pressure goes to zero and coolant jacket is still pressuized.
The coolant then flows into the oil through the same crack.
It is more common to have coolant in the oil than oil in the water, since the coolant molecule is smaller than the oil molecule and the collant passes through crack easier than the oil.
Gas bubbles in the radiator as seen by removing the radiator cap is a result of a leaking head cover gasket, where the high pressure combustion gas passes through the ruptured gasket into the coolant jacket.