Songs on the album sound down and dirty, rough and loose. The production is often very hot- not really maxing out, but just packed in really. Songs are quite thick, with every sound vying for attention of the ear. This isn't really unpleasant, as it suites the feel of the music quite well.
Songs like "Things Have Changed" change up halfway through, and have tempos that speed up while staying tight instrumentally. Little tricks like this keep things interesting and raise their sound above just basic blues rock.
The particular style that evolves with the vocal and guitar combo can sometimes be comparable in pacing to White Stripes music, though the male vocal's timbre never reaches the screechy high octaves Jack White is known for.
"Odessa" by Discount Guns is available for download with the single "The Water" offered for free, via their Bandcamp page.