150+ IP, sub-2.00 ERA, 9.0+ SO/9 (Since 1900)
1964 Sandy Koufax (Dodgers)
1968 Luis Tiant (Indians)
1968 "Sudden" Sam McDowell (Indians)
1971 Tom Seaver (Mets)
1986 Mark Eichhorn (Blue Jays)
1997, 2000 Pedro Martinez (Expos, Red Sox)
2010 Josh Johnson (Marlins) 155 IP, 1.97 ERA, 9.06 SO/9
Surprisingly, the only pitcher on the list to win the Cy Young award in one of these seasons was Pedro Martinez, in both 1997 and 2000. Tom Seaver came in 2nd in 1971, Denny McLain got all the votes in 1968, and Dean Chance took the only Cy Young Award in 1964.
Eichhorn's season was interesting in several ways. It was his rookie season, and he finished 3rd in Rookie of the Year balloting and 6th in Cy Young Balloting despite not making a start and having only 10 saves. It is (and probably always will be) the only season in ML history where a pitcher tossed over 150 innings, made 0 starts but did not have over 10 saves (he had 10).
There were nine other seasons from 1950 (Jim Konstanty's Cy Young season) to 1986 (including two by Mike Marshall) that had a pitcher toss over 150 innings, have 0 starts, but they all had more than 10 saves (Eichhorn had the only one of the bunch, though, with over 9 SO/9).
Josh Johnson currently has an ERA of 1.97, so he's one bad inning from going over 2.00. Even if you take the ERA out to 2.20, these are the only additional names added:
Sandy Koufax 1965
Sam McDowell 1965
Pedro Martinez 1999
Roger Clemens 1997
Zack Greinke 2009