Ahem. In LOTR and Middle Earth there is only one God, Illuvatar, IIRC. Illuvatar was served by lesser beings of his own creation, the Valar, which could be considered angels, devas, demigods, godlings, or whatever your imagination wanted to consider them (I just thought of them as Valar...). During the process of creation the greatest of the Valar rebelled. He became Morgoth and, at the end of the Second Age, he was defeated by the Valar and the Maiar and expelled from creation (the elves had been fighting fruitlessly with him throughout the First and Second ages).
Below the Valar in power were Maiar. Sauron was a Maiar in the service of Morgoth and survived Morgoth's fall to cause trouble in the third age. Gandolf, it is hinted at in the book and stated blatantly in the movie is a Maiar (I think in the Silmarillion it is hinted that Gandolph actually a Valar!). In any case, Gandolph's (and Sauron's) magic comes from himself.
Read the books: The Hobbit, LOTR, The Silmarilion, the Unfinshed Tales, etc. It would be a good use of your time. As soon as the girls can hold still for an episodic tale, their going to get the Hobbit (right after Wind in the Willows...).
Gandalf/Olorin is a Maia, not a Vala. He is of the same order as Sauron, Curunir (Saruman), and Melian (Arwen's great-great-grandmother, I believe).