Navion pilot reported having an NMAC with NORDO King Air on final requiring evasive action to avoid a possible collision.

Narrative

Flying VFR from ZZZ1 to ZZZ. Approaching from the northwest I heard on GUARD (Which I try to monitor as much as possible) 'KingAir will be doing approaches at ZZZ 15 miles out'. At this time I was also listening to ZZZ CTAF XXX.X; I made position reports at 5 miles and as we entered the downwind for Runway XX. I thought I heard KingAir at others times but was mixed with UNICOM chatter; that was when I realized that the KingAir pilot was ONLY listening and transmitting on Guard; and; that none of the other pilots in the pattern were hearing her because they were not monitoring Guard. I assumed that were still a few miles out and entered downwind; and announced position on UNICOM. As I turned left base; we saw the Kingair on low final; in a collision course as I rolled out of the left turn I had critical decision to make and executed a hard right turn as that would put me on the KingAir's tail as it went by me. I called out on UNICOM that we were 'diverting for King Air' and recovered to level flight and got lined up for Runway XX again; and landed uneventfully.I heard the other pilots on UNICOM commenting that the KingAir was not talking on the frequency; they were bewildered.I hope this helps someone. I have learned that if I hear a KingAir flight; I will just avoid the whole area until they are done.