I’ve seen a Beeman advert that referred to a “deluxe” Omega, but it looked just like a standard Webley Omega. Probably just the advertising. The standard beech stock was deluxe compared to American manufactured airguns of the time, so they probably just labelled it as such.
If there ever was a factory deluxe (i.e. walnut) version of the Omega I’d love to see one!
Cheers
Greg