Single Engine Pilot reported encountering a wind shear on final; not lining up with the center line; loosing airspeed; encountering a stall and landing partially in the dirt. In the process of missing the runway the pilot stated the aircraft damaged a MIRL; There was no damage to the aircraft.

Narrative

I was flying a C172M into ZZZ. No weather reporting station so we made a low approach for [Runway] XX; strong tailwind led to an early go-around on the high fly-over. Noticed the wind cone pointing straight down [Runway] XY. Set up for an alternate mid-field entry for XY to do a low fly-over. On final crossing over the approach end; we suffered a 30 ft. drop in altitude due to windshear. This led to an immediate go-around; unfortunately; while executing the go-around we suffered another wind shift which knocked us out to the north of the runway about one to one/half wing span from the center line. This also led to stalling the plane roughly 30 ft. above the ground. With 1;000 ft. remaining I pitched down and realized we would not clear the 60 ft. trees at the end of the runway so I then pulled the power and put use down on the runway. But due to being knocked off of the center line; only half of the plane made it onto the runway. The other half was put into the dirt. On the ground; I took immediate actions to get back onto the center line to execute maximum breaking. We came to a full stop with 250 ft. remaining. During our time on the dirt; we did take out one of ZZZ MIRL on the north side of the runway. After a full inspection of the plane; no structural damage was noticed. We attempted to contact the Airport Manager; no answer. Still in the process of getting a hold of him. While on the ground we watched the wind cone and it would regularly shift 30-40 degrees fully erect.