They think they sound like the Violent Femmes and the Lemonheads. Other people compare them with The Decemberists and the Moldy Peaches. I’d agree with all the above and add the White Stripes and the Fiery Furnaces to the mix.
The music has a traditional edge, but deals with modern (yet universal) subjects. Both singers can sing, and it sounds like they would be amazing in a live setting (anywhere from a concert hall to a camp fire).
My favourites are "Gold Fever" and "Ballad of a Jailbreak Wedding", although every song is strong.