Does the Vagus nerve belong to the Sensory-Somatic or Autonomic system?
Autonomic nervous system.
Vagus is 10th cranial nerve; it is a mixed nerve.
It belongs to autonomic nervous system. To be more specific, vagus is parasympathetic outlet.
Vagus has very limited sensory role, some sensory fibres arise from root of tongue and epiglottis , etc.
It contains motor fibres like all nerves of autonomic system; Branches of motor fibres of vagus extensively supplies respiratory, cardiovascular and gastrointestinal organs . It is the longest cranial nerve.
Motor nerve from vagus also controls movement of laryngeal muscles for production of sound.