There are several companies other than Rolex and Seiko that make their own movements. Citizen makes automatic movements under the Miyota name; and (my personal favorite) Poljot manufactures everything but their automatics in-house.
There are a few other makers who use in-house movements in particular models.
Of course, most of the real big-dollar brands (Lange, Patek, AP, etc.) produce their own movements as well.
The issue of ETA movements is generally an ambiguous one, mostly because the watch manufacturers want to maintain the image that their movements are being made one by one by an old Swiss craftsman in a chalet somewhere in the Alps rather than by modern machinery.
There are some brands (TAG, for example) who use basic off the shelf ETA movements in their products, with any modification being limited to an engraved rotor and other cosmetic touches.
There are other brands, such as IWC, who completely gut the ETA movements and replace most of the important parts with better ones of their own manufacture.
Omega falls somewhere in the middle. They do get their basic movements from ETA and modify them, but not as extensively as IWC does. Besides cosmetic improvements, Omega replaces the winding rotor with a proprietary design with a different bearing setup. They also replace the automatic bridge with one of their own design which reduces the movement height and friction. Standard ETA movements use a metal bearing to hold the barrel in place. Omega replaces this with a pair of jewels, which serve to increase accuracy and power reserve.
I'd say thats some pretty significant modification, certianly enough to make the product unique.
Also, since Omega and ETA are sister companies under the Swatch Group you could consider ETA movements to be of Omega manufacture anyway, but that might be pushing it a bit.