Yes, Badger hoses will fil the Omni. Thayer and Chandler airbrushes are made by Badger now.
Badger has two styles of hose. The vinyl hose has 1/8" connections on both ends and the braided hose has a 1/8" connector on one end and a 1/4" NPT connection on the other. To connect the vinyl hose to a compressor or tank you'll need an adapter to go from 1/8" to 1/4". Badger sells them for about $4 or so. IT's on this page: http://www.badgerairbrush.com/access2.htm and is part no. 50-023