The Gibraltar international sealed a deserved victory with second half goals following Ben O’Hanlon’s header from a corner in the first half.
The Glassboys, now unbeaten in three and off the foot of the table, enjoyed a lot of possession and made it count with a succession of chances.
Styche doubled the lead just past the hour mark with a fierce shot past keeper Charlie Horlock.
The 32 year old then wrapped up the points with another powerful strike in the last minute.
Hitchin had a goal ruled out for offside but the hosts were no match for Mark Yates’s improving Stourbridge side.