Why does oil float on water? This might be a silly question but I want to know why oil actually floats on water. I tried to explain it to myself using Archimedes' principle but that didn't help. 

Archimedes’ principle, physical law of buoyancy, states that any
  body completely or partially submerged in a fluid (gas or liquid) at
  rest is acted upon by an upward, or buoyant, force the magnitude of
  which is equal to the weight of the fluid displaced by the body.

I don't get how Archimedes' law is valid in oil-water case, because oil and water don't even mix so there's no displacement of water hence no byouant force is exerted. So what keeps substances like oil which are less dense than water floating atop it?  
 A: "...because oil and water don't even mix so there's no displacement of water hence no buoyant force is exerted." 
This is where you are misunderstanding. There is a displacement. Wood doesn't mix with water either, yet it displaces water and it floats. With oil, there is a slight depression of the lower surface, between the oil and water, where the displacement occurs.
A: Water is heavier that oil for the same unit volume due to its higher density. Due to its larger mass, it settles at the lowest level to have the smallest potential energy and it able to do so as water is fluid. So water body is positioned below the oil body.
A: As I see it, this happens because any mixture of oil and water is unstable. Let us consider a drop of oil, in a glass of water, and pretend that the drop of oil is solid. It will float, with a part submerged. Now let us give back to the floating part its liquid properties: it will spread on the whole surface of the water.
I think now we can repeat the reasoning for the submerged part, pretending again that it is solid, while we consider the water and the floating layer of oil as liquids. There is a buoyancy force on the submerged part that brings some of it above the water/oil interface.
I did not think carefully about how to complete the reasoning, but it could well be that this leads to all of the oil to form a layer above water.
A: If you agitate an oil water mixture and then stop, you can actually see small blobs of oil moving up through the water as the separation occurs.  So this seems just like normal buoyancy.  Same with bubbles of gas.
