In the minor leagues that was Ron Necciai of the 1952 Bristol Twins who struck out 27 batters in a no-hitter against the Welsh Miners in an Appalachian League game.
In MLB that was Nolan Ryan of the 1973 California Angels who struck out 17 batters in a no hitter against the Detroit Tigers.
Cy Young
Sandy Koufax
Mark Buerhle
Randy Johnson
Roy Halladay
Randy Johnson - 19
you do not say that the pitcher is pitching a perfect game
In David Wells' perfect game on May 17, 1998, he struck out 11 Minnesota Twins batters.
The Tigers team record for most strikeouts in a game by a pitcher is 16 by Mickey Lolich. He struckout 16 California Angels on May 23, 1969 and 16 Seattle Pilots on June 9, 1969.
Any team that had an opposing pitcher throw a perfect game or no hitter
15.
9
11
22
7
14
For the Los Angeles Angels single game records, the pitcher with the most strikeouts in one game of nine innings is Nolan Ryan with 19. The pitcher with the most strikeouts in a game with extra innings is also Nolan Ryan with 19. The pitcher with the most strikeouts in one inning is Chuck Finley with 4. The record for most strikeouts in a game by the team is 18. The player with the most strikeouts in one game while batting is Dallas McPherson with 4. The most strikeouts by a batter in a game with extra innings is Billy Cowan with 6.
bob gibsom
Randy Johnson - 19
97 K's by Akio Nakamura for the Yankees in June 2012. He had 6 starts, 6 complete game shutouts, 6 wins, 1 perfect game, an ERA of 0.00 and 97 strikeouts. A feat never to be accomplished again.
Roy Halladay just did it yesterday (No hitter was in postseason though)
On June 13, 2012, Matt Cain of the San Francisco Giants became the latest pitcher to throw a no-hitter. It was also a perfect game.