Injury of which of these nerve cause vocal cord paralysis?
When both recurrent laryngeal  nerves are interrupted,  the vocal cords lie in the cadaveric position in between abduction and adduction and phonation is completely lost. Deep breathing also becomes difficult through the partially opened glottis.
When only one recurrent laryngeal nerve is paralysed, the opposite vocal cord compensates for it and phonation is possible but there is hoarseness of voice.  There is failure of forceful explosive part of voluntary and reflex coughing.

BDC Head and Neck 6th Ed P:258
Recurrent laryngeal
External laryngeal
Internal laryngeal
Superior laryngeal