It's not quite accurate to say that a liquid "mixes" with oil. Oils are generally nonpolar, meaning they don't have a positive and negative end like water (which is polar). This difference in polarity makes them immiscible, meaning they don't mix.

Instead of mixing, some liquids dissolve in oil. These are also nonpolar liquids, like:

* Other oils: Vegetable oils, mineral oil, etc.

* Solvents: Acetone, toluene, kerosene, gasoline.

* Fats: Butter, lard, etc.

Water and oil don't mix because the water molecules are attracted to each other (hydrogen bonds) and "push" the oil molecules away.

Important Note: Some substances can act as emulsifiers, which help to temporarily suspend tiny droplets of oil within water, creating a mixture that appears mixed but is actually a temporary suspension. Examples of emulsifiers include soap and egg yolks.