Where does the loyalty of the eagles originates from?

To who/what are the eagles loyal? And why?

It seems the eagles are loyal (to some extend) to Gandalf and to the men, dwarves and elves. Why? What do they get in return for that? Are there documented battles where the men/dwarves/elves helped the eagles? After all, a coalition is only maintained if every party has benefit from it...

It sometimes looks as if Tolkien uses the eagles as a deus ex machina: a solution in case the war seems totally lost. Is there anything known about what the eagles possibly/probably represented in the real world?