PA-28 Flight Instructor with student reported a bird strike while in the traffic pattern. Flight crew returned to safe landing.

Narrative

I was flying in the traffic pattern at night with a student. We were given a takeoff clearance for runway XXR at ZZZ. We were instructed to takeoff on runway XXR and make left traffic for runway XXL (the north parallel runway). We were at approximately 700 feet MSL turning crosswind to downwind when we heard a sudden thud and felt an impact of some sort. We initially thought that our baggage door popped open during flight; but we determined that it did not. Our airplane felt slower and sluggish; but we had full control authority of our elevator and ailerons; and rudder authority was fine. We also had full engine power. Both my student and I also soon noticed a weird smell emanating the cockpit. Unaware of what happened; I informed tower that we had something happen and I requested priority for landing. We were cleared for runway XXR; but I requested runway XXL as we were on downwind approaching abeam our intended touchdown point and I wanted to land as soon as possible so that I could better investigate our situation. Tower cleared us to land on runway XXL. Upon vacating the runway after a safe landing; we were instructed to taxi back to our ramp via taxiway 1 and taxiway 2 hold short of runway XXR. While taxiing; I opened the door and looked behind me at our tail and noticed that there was a very large bird hanging off of the top of our vertical stabilizer. I informed tower of the bird strike. Both myself and my student were fine and we reported the incident to tower and our company. I took multiple pictures and video from every angle I could after we parked the airplane and tied it down. The vertical stabilizer suffered significant damage in the form of a very large dent on the front side of the fin and a broken beacon. The VOR antenna somehow managed to come out with no damage despite the bird being impaled on it.