Damage depends on ammo. Are you still firing bullet stones ? I forget which gadgeteer level is needed to fire crossbow bolts, but an omnigun with the repeater and blinding attachments firing Lightning Bolts (10-40 damage?) is fairly devastating. Be sure to build strength and vitality, and wear vitality-enhancing items.Also be sure to right-click on the Omnigun and find out what improvements the gadgeteer has added at level-up.
At level 7 you haven't seen much of the world. Monastery, Arnika Road and Arnika are about all you can survive right now. Give the game a little more time and feel free to ask for hints.