[Essex]

Also, weren't the Eagles created by Manwe as some form of 'spirit'. i.e. akin to Gandalf's Istari?

Just hunting in the Silmarillion and I've found this about Manwe:

Spirits in the shape of hawks and eagles flew ever to and from his halls; and their eyes could see to the depths of the seas, and pierce the hidden caverns beneath the world. Thus they brought word to him of well nigh all that passed in Arda

And also regarding Manwe again:

Did not thy thought and mine meet also, so that we took wing together like great birds that soar above the clouds? That also shall come to be by the heed of Ilúvatar, and before the Children awake there shall go forth with wings like the wind the Eagles of the Lords of the West.' Then Yavanna was glad, and she stood up, reaching her arms towards the heavens, and she said: 'High shall climb the trees of Kementári, that the Eagles of the King may house therein!'

Also, regarding the size of the Eagles (well ok, at least Thorondor)

For Manwë to whom all birds are dear, and to whom they bring news upon Taniquetil from Middle-earth, had sent forth the race of Eagles, commanding them to dwell in the crags of the North, and to keep watch upon Morgoth; for Manwë still had pity for the exiled Elves. And the Eagles brought news of much that passed in those days to the sad ears of Manwë. Now, even as Fingon bent his bow, there flew down from the high airs Thorondor, King of Eagles, mightiest of all birds that have ever been, whose outstretched wings spanned thirty fathoms; and staying Fingon's hand he took him up, and bore him to the face of the rock where Maedhros hung.

And finally,

Then men grew afraid. 'Behold the Eagles of the Lords of the West!' they cried. 'The Eagles of Manwë are come upon Númenor!'

So I think these few examples show that the Fell Beasts (and the Nazgul, without their Lieutenant) were NO match for the Eagles of Manwe………