I think that the importance to which Christians place the philosophical notions of ''the omnis'' is exaggerated by the New atheists.
What are you basing this view on?
They are as Gerald Priestland would say, saddling Christians with a God they don't subscribe to anyway. So as far as that is true, New atheists are making a strawman argument.
So is it about importance or belief - do make up your mind. If (some) Christians believe in a god of the omnis, they aren't being saddled with it, are they? As I said, unless you want to claim that there aren't significant groups of Christians who believe in a god of the omnis, then it isn't a straw man.
As Steve has pointed out these ideas are more greek philosophy.
It's origin really doesn't matter to the point.