In three categories: Rock, Religion, Romanticism.
Cream, Strange Brew
Doors, People are Strange
Doors, Strange Days
Mickey and Sylvia, Love is Strange, 1956
Stanley Bros., Rank Strangers. Utterly deplorable.
Eva Cassidy, Wayfaring Stranger
Johnny Cash, Wayfaring Stranger
Frank Sinatra, Strangers in the Night To be is to do (Socrates). To do is to be (Sartre). Do be do be do (Sinatra).
Barbara Lewis, Hello Stranger, 1963. 1963 was arguably the best of the '60s years for pop compositions.
Emmylou Harris, Hello Stranger. Same title, different song. This one goes out to Mary Kay F-D. Remember the Fall of 1980, Mary Kay?
Get up, rounder/Let a working girl lie down/ You are rounder/And you are all out and down.
Carter Family version from 1939.
Acker Bilk, Stranger on the Shore. A memorable '60s instrumental. More here.