PA-28R Flight Instructor reported a NMAC in the traffic pattern with a flight of 3 GA aircraft at a non-towered airport and took evasive action to avoid a collision. The Instructor reported the aircraft were not broadcasting positions on CTAF and only one had ADS-B data displayed.

Narrative

I was flying a Piper Arrow; at ZZZ [airport] with a student working on a complex endorsement. My student was at the controls and we were established in the traffic pattern for runway XX and making normal traffic calls on CTAF. When we got to about the mid-field downwind position; my student and I noticed that there were three aircraft headed directly at us at an extremely high speed on ADS-B; one of which did not show up with a callsign. We had not noticed them earlier because they had not made any transmissions on CTAF; so I had assumed that they were in the practice area. My student got the airplanes in sight before I did; and he judged that the safest course of action was to immediately make our base turn to stay clear of them; which I agree was the best option. After we started turning left base; I got the three airplanes in sight and saw that they were all Vans RVs or similar in a tight formation. I estimate that they came within 100 feet of us. After I visually identified the airplanes; I realized that they had made a single call as a 'flight of three RVs'' before we had even begun our takeoff roll saying that they would be 'flying over the town and then heading east'. I cannot remember if those were the exact words that were used but that was the only information that their transmission contained. After I saw the traffic; I asked them on CTAF if they knew that they were in the downwind and one pilot responded to me saying that they were 'north of the downwind and monitoring CTAF'; this is factually false since the airplane that I was flying was on the downwind leg; and they were right next to us. Regardless; monitoring CTAF without broadcasting while being anywhere near the traffic pattern is grossly inadequate. After we landed; we were taxiing back to depart XX again and I saw them on an upwind for XX. Additionally; they were using CTAF to converse with each other about trivial items. I specifically heard one tell the others to turn their smoke on and then all three airplanes started releasing smoke. I did NOT hear them make any relevant; safety related; calls such as upwind; crosswind; or downwind. When we got to the end of XX; we saw them; visually; all on an extremely tight; low; and fast downwind; so we decided to wait for them to land before departing for separation. While waiting; I was looking at my ADS-B to confirm that there was no other traffic in the pattern that was not talking on CTAF and that I had not visually seen. I only saw one airplane on ADS-B even though I had visual contact on the other airplanes; so I am assuming that they turned their transponders off so that I would not be able to see their registrations. I believe this near mid-air was caused by insufficient training on the part of the pilots in formation and their failure to recognize and correct their macho; invulnerable; impulsive; and anti authority hazardous attitudes. I believe that my student and I took all the appropriate actions that were available to us.