When teaching a class on how to draw animals, we covered mostly graphite and colored pencils, but one of my students wanted to draw with crayons. It was fun cracking open the box of Crayolas and giving the class a demonstration. I shared the illustrations I had done for the book, and we analyzed the characteristics of drawing with crayons.
Whilst most colored pencils are wax based, some brands use an oil based lead, like Faber Castell's Polychromos. These pencils are very soft to apply color so will cover every fibre of the paper with their bright hues, but they are also very expensive and should only be considered if you are looking to take your art to the highest level.