How to describe the "oil flying out of the pan" when cooking?

"Spatter" is a good word for that.

Here's the definition I'm using from Webster's Third New International Dictionary, Unabridged:

To jet or spurt forth in scattered drops

This is one of the definitions for the intransitive sense of "spatter."

A specific term for that is oil "spitting" which I like also because of the onomatopoeia it creates.

According to The Chambers Dictionary, in the meaning nearest to the present context, spatter is defined as "rain down or fly about", while sputter is "spit out or throw out moisture in scattered drops". I think that the latter applies equally well to hot oil or melted fat, as it does specifically to molten metal in the technical term sputter deposition. Thus the most precise word here is sputter.