I still don't understand why they didn't just take the birds from the start, and all the way to the end. It would've saved a lot of trouble, not to mention hard disk space.
And this is what happens when you have a fan-made film and they decide to throw in so many references to other things they miss the subtleties. From what I remember (I'm re-reading it right now, but haven't got to that bit) the Eagles are incredibly arrogant (which is sort of understandable, living on top of the world, being servants of the gods, there to protect the fauna of Middle-earth from nasty things). They pretty much refuse to associate with anyone and certainly wouldn't go all the way across Eriador just to help a bunch of dwarves get some gold and land back. That they talk with Gandalf (and help him in FotR) show just how must respect they have for him.
From what I remember, they come down to the woods (where Thorin & Co. are being attacked by the wargs) because the wargs were having a big meeting (that just happened to be taking place there anyway) and the eagles wanted to know what was going on. They help the dwarves, Bilbo and Gandalf partly out of respect for Gandalf and partly because they really hate the wargs (and orcs). But even then, they simply carry them up to their eyrie, talk for a bit, then take them back down to plains (but a bit further away). There's no moth, and no "pale orc." Iirc there is a white warg, though, who is the leader of the various warg clans.
As for it all about them getting into trouble and Gandalf rescuing them... it's only 3 times in the book (4 if you include the eagles) that he does that, but then that's what he is there for. Plus it, perhaps, makes it more interesting later on when they have to save themselves without Gandalf's help, and Bilbo starts to really shine.