Oil and water don't mix because water molecules have a small positive charge at one end, and a small negative charge at the other end, so they stick to each other. But oil molecules are without charge, which causes them to be attracted to each other more than water.
Oil floats on water since it is less dense than water, according to the National Science and Technology Center of Australia. Water molecules are attracted to each other because they are polar, but oil molecules are non polar. Animals that live in rivers or cold environments keep warm because their skin or feathers have an oily coat to keep the water away.