Guitar strumming, unorthodox rhythmic drumming, and, most importantly, the vocals that carry out seemingly callous yet powerful lyrics: they may well be the exact impression listeners can be called to when it comes to The Dodos.
As the cover picture suggests, The Dodos are made up of the duo Meric Long (guitar and vocals) and Logan Kroeber (drums). The two rock their instruments to produce something that is distinctively heard, nonetheless, beautifully intertwined harmony, instrumental-wise.
Wikipedia suggests that this style is best categorized psych folk and/or Baroque pop, and the following links are to introduce such sounds to you.
Companions - The Dodos
This is from the album "No Color", which, to my personal opinion, by far, best shows the very elementary fabric that the kind of music this band produces.
Winter - The Dodos
"Visiter" is another album that contains many definitive sounds for the band. The simple rhythmic accents on the drums alongside the mandolin in the intro seeps deeply into one's aural synapse when one hears this song for the first time.
The Current - The Dodos
From their most recent album "Carrier", the song advances the band's sound even further with more layers of harmony and melodies.