Ever seen those cocktails where they "float" the alcohol on top of the sweet, sugar and water based liquid underneath?
Or a "float" coffee, where the fatty emulsion (cream), sits atop the denser water and sugar solution underneath?
In both cases, the less dense (alcohol or fatty cream) is poured in carefully and slowly so that it sits on top of the more dense water-based liquid.
In your barrel of oil scenario, as stevie says, it depends how quickly or slowly your pour it in, from what height, in a jet, a big spalsh etc. etc.
If you pour it in carefully and slowly, only oil will overflow the barrel rim. Chuck it in at once from a great height, and a mixture of oil and water, (and more than 50 litres at that) will overflow.