Cessna 206 pilot reported an NMAC with a Cessna 340 during final approach to a non-towered airport. The Cessna 340 pilot was not making radio calls due to having an inoperative radio system.

Narrative

A near miss occurred upon final approach when landing on Runway XX at ZZZ airport. While I was in the pattern I heard the Pawnee [Aircraft Y] tow pilot muttering 'carrier only!' He has an accent and over the roar of the Aircraft Y engine I couldn't discern exactly what he was saying. His radio was clipping in and out; I brushed it off thinking he was attempting to communicate with another aircraft; which also has a bad radio and uses a handheld radio currently. I made my traffic pattern calls clear and watched my avionics comm radio make the transmission 'T' Symbol on comm 1. I didn't see anyone on my ADS-B sentry device. I had been communicating with approach five minutes prior and other aircraft earlier that morning so I knew it wasn't my radio. I continued my downwind looking for traffic but couldn't see anything. I repeatedly heard Aircraft Y pilot; make calls that were unreadable and brushed it off that he was talking to the glider in tow and making calls to land on dirt runway which is no factor for landing [Runway] XX traffic. There was a jet inbound from the south making calls to land on [Runway] YY which I found odd because winds were calm and if she was to the south she would need to overfly and enter the pattern for that runway. It is common practice and culture to give jets the right of way when within 10nm if on final. It is of my biased opinion that the pilot seemed new to the airport.I made my base call descending out of 5;500 MSL then turned final at 5;100 MSL. While on final out of my peripheral a green orb entered. I couldn't believe my eyes a multi engine plane [Aircraft Z] was nearly right on top of me descending down. I pitched the nose down and flew an upwind to the left; non standard; because If I turned right my plane could have collided with him.I called my 'go around' and informally communities with Aircraft Y pilot 'did you see that!'. He said that he was trying to tell me there was a Nordo in the pattern. I flew the pattern had to negotiate with the jet; let her fly straight in XX and extended my downwind to be courteous. I landed and tracked down the pilot to inquire about the near mid air collision.When I talked with the pilot of Aircraft Z; He seemed rather out of it; said his leg had 'fallen asleep' and that he was having a hard time walking over. I exclaimed to him that he wasn't talking on the radio and he almost ran into me. He apologized sincerely and we had a fruitful conversation of potentially flying together in the future if he needed a copilot once I receive my multi engine rating. He told me he flew into ZZZ airport to get his radio fixed and that currently it is inoperative. Since he was a low wing and me a high wing; it made for the nearly deadly situation. I will be that much more vigilant in the future especially turning base to final looking for traffic. ZZZ should think more seriously about getting a control tower.