Some sites with songs of the Spanish Civil War:
Himnos y canciones de la guerra civil, with songs of all participants on the republican front, with tunes.
La guerra civil Espanola (canciones)
Rojo y azul
All above with texts and tunes.
Canciones de la Guerra Civil y la Resistencia - tunes only; link to Woody Guthrie's Jarama Valley unfortunately not found, but "The young man from Alcalá" is in American English with a slight Texan touch.

For further research try Google with canciones +guerra +civil, "Spanish Civil War".