What is the difference between natural, preternatural and supernatural?

Natural: is the action which is proper to the structure of nature. When we speak of nature, we are referring the nature of the material universe.

Preternatural: is the action which goes beyond the structure of the nature of the material universe. The fruit of the action of an angelical or demoniacal nature is said to be preternatural. The word comes from "praeter naturam", beyond nature.

Supernatural: is the action which goes beyond any created nature. This form of activity belongs only to God.
Material nature can bring about surprising things, but it will always be according the the laws of the material cosmos. The devils can levitate an object in the air, transform something instantaneously, etc. They can do things which go beyond the possibilities of the material world, but they cannot go beyond the laws of their angelical natures, because they cannot do everything. They cannot do everything even in the material world. God, however, can create an organ from nothing; a devil cannot.

These differences are also valid concerning those things that happen in our soul. For example, a beautiful scenery can remind me of God's beauty, which is something natural. While an angel or devil que send inspirations directly to my mind, God goes beyond that, since he can send spiritual graces (repentance, thanksgiving, etc.) to the most inner recesses of my spirit, bringing about radical changes in a split second. All workings of grace are supernatural. And grace is always sent directly by God.