The GLH was the original Shelby designed hot hatch, and the basis for his in-house GLH-S (Goes Like Hell, S'More) special that was sold directly from Shelby. The Omni GLH, on the other hand, was sold directly from Dodge dealers and probably purchased by accident a few times by old folks looking for the nicest Omni on the lot.
Power in the Omni GLH comes from a hopped up version of the Chrylser K-car 2.2 liter inline-4 the Turbo I. In GLH spec it is boosted to 146 horsepower, which should push the 2200 lb Omni around with some gusto.
Don't expect the interior of the Omni to impress anyone, but this one could use a new set of seats. Skip trying to find a re-upholstery shop to recover those stock seats (it'll cost a fortune) and instead look for something used on your local craigslist. Maybe Recaros from a 320i?
See a more practical and ridiculous car in one package? firstname.lastname@example.org