The Iraqi car market is a pretty difficult one to approach, with not much recent YouTube video material and no clear and apparent winner in the sales. So I will venture a very rough speculation, that would see the Toyota Hilux, Hyundai Accent and Great Wall Deer (an old gen Hilux) dominate the rankings.
The Toyota Corolla, Chevrolet Aveo, 2005 Hyundai Sonata (probably imported from Egypt), Toyota Camry, Nissan Sunny and Great Wall Sailor (an old gen Nissan Frontier) are also strong in Iraq. The Chinese brand Great Wall is indeed making some inroads in the country. Interestingly, the Iran Khodro Samand and Iranian-built Peugeot 405 also seem to have some success.
More info and pictures below.