Why would all the oil leak out of a car?

You have a leak and a large one. If you or a cheap store just changed oil, then they may not have attached the Oil Filter or the Oil Pan Plug correctly. If you leave off an O-ring or don't lube the gasket on the oil filter, then it could leak. Generally this will not leak very fast. The oil pan plug is at the bottom of the oil system and it would leak out all of the oil. Check your radiator water. Sometimes an engline will leak oil into the coolant system and it will be carried to your radiator. This will turn the water a chocolate milk color.