As electric guitars and speakers did not exist at the time of the First World War, we can assume that they do not exist in the world of Guns Of Icarus, personally, I believe that:
-The Yeshans would listen to, if anything, propaganda music. Music telling the citizens of the Yesha Empire to work, work and work until their hands and bloody and their spirits broken. This would sound similar to the music played in North Korea in the real world.
-The Arashi would listen to tribal music, or, as Riggatto said, Middle Eastern music.
-The Merchants would listen to a mixture of the other factions, trading with them not only their possessions, but also musical ideology.
-The Chaladonians would listen to sort of ancient Chinese music, possibly pipes, etc.
-The Angleans would listen to turn of the last century music, classical, and perhaps would be in possession of the few working gramophones, able to listen to pre war music.
-The Baronies would listen to Celtic music, similar to the Nords of Skyrim, their songs would be rich with tales of previous victories.
