Flight Instructor reported evasive action to avoid a helicopter during landing. Reporter stated communication issues added difficulties to the incident.

Narrative

I was 5 miles east of ZZZ I made a position report indicating I was maneuvering for a left 45 degree entry for a midfield downwind entry into Runway XX at ZZZ. My student flew east and was roughly 3 miles north of ZZZ when I made a position report again indicating we were going to fly southwest bound for a left 45 degree entry for the midfield downwind into Runway XX at ZZZ. Upon this time I heard a helicopter call that they were turning right crosswind and making right traffic to Runway XX (helicopter was in sight). I announced my aircrafts tail number stating I was left midfield downwind for Runway XX and soon after I heard the helicopter state they were on the right downwind and were going to 'autorotate' for Runway XX. My student continued flying the pattern and turned left base after I made a position report stating we were turning left base to Runway XX. I scanned for traffic but lost the helicopter. I announced on the CTAF we were turning final to Runway XX and instructed my student to proceed ahead and land. As we touched down on the numbers I was watching for my student to maintain directional control when we both noticed the helicopter's landing skids come into our view above us and moving forward. At this time my student went full throttle and maintained directional control left of Runway XX center line nearly off the runway and we accelerated past them holding the nose down so our tail would not be hit by the rotor blades. After a few seconds we started to climb out and on the upwind we were harassed on the CTAF because the helicopter crew believed we made a straight in approach. At this point I explained how I had made multiple position reports stating how far the aircraft was away from the field; our intention of entering the pattern; and at what point in the pattern we were currently at. The helicopter made 'takeoff'; 'right crosswind'; and 'downwind with intention to auto rotate' calls at no point was there a position report on their end indicating a 'right base' or 'final' call to Runway XX. After the exchange of words across the CTAF my student and I made a left crosswind departure and headed back to the west. This could easily be avoided next time by the announcement of proper position reports in the traffic pattern.