The name Orc

[Gwaihir the Windlord]

Actually, Mans, Guinevere is correct. If Tom Shippey is not a valid enough source, JRRT himself should be.

The Grey-elven form is orch, plural yrch.
I originally took the word from Old English orc [Beowulf 112 orc-nass
and the gloss orc = pyrs (?ogre?), heldeofol (?hell-devil?)].
This is supposed not to be connected with modern English orc, ork, a name applied to various sea-beasts of the dolphin order.

Obviously he does not mean demons in the modern, Devil-hell sense (red skin, horns, forked tail, manic grin etc), as Kaiserin says, but demon in the sense of an evil and Morgoth-sourced creature. No mention of your Ancient Greek derivitive is to be found.

It was an appreciable suggestion, but it looks like Old English -- a source of quite a lot of Middle-Earth linguistics -- was in fact the inspiration for this word, thereby proving that it could not have been Greek.