what is the reflex pathway for sneezing?

Answer 1

Well the "sneezing centre" is almost certainly in a part of the brain stem called the medulla (specifically the rostral dorsolateral pontomedullary area). Indeed, electrical stimulation of this area makes animals sneeze automatically, and people who have had strokes or other forms of damage to this area report not being able to sneeze properly. Cranial nerves (the facial nerve mainly) project from the nose, directly to the medulla.

I don't think people know what happens after that, however if it is like other things (coughing, yawning, vomiting), the medulla will activate some kind of central pattern generator (a complex of neurons that orchistrates a particular complex behavior), which then makes the sneeze happen.