They don't dissolve. Instead, each of these particles is suspended in the oil and vinegar but still visible. This is called a suspension . One special kind of suspension is called an emulsion . An emulsion happens when a watery liquid is mixed with an oily, fatty, waxy or resinous liquid in such a way that the oily liquid is suspended in tiny droplets in the watery liquid.
Milk is an example of an emulsion.
Paint is a special type emulsion called a colloid . When emulsions are spread out in a flat thin layer, like paint on a surface, the oily, sticky emulsifier is able to harden. Back in the early 1400's, most painters used paint made by grinding up bits of earth and minerals and mixing it with egg yolk and water to make a paste. This paint was a colloid because bits of color or pigment were suspended in egg yolk, the emulsifier, which was suspended in water. This type of paint was called egg tempera.