On 6/20/1961, Bill Monbouquette allowed 8 runs over 7 innings and still managed to pick up the win. His final line: 7 ER, 7 BB, 7 SO, 8 H, 3 HR. 

In 1993, Tony Pena had only 55 hits in 304 at bats. His season average was .181.

In 1992, Tony Fossas pitched 30 straight games in relief without giving up a run. His streak ran from 6/20-8/29/1992. 

Jerry Stephenson pitched a complete game on 6/21/1968—and the Red Sox lost by a score of 4-10. Seven of the ten runs were earned. Stephenson struck out seven, walked five, and gave up thirteen hits.

Tom Carey is the oldest player to ever play second base for the Red Sox. He was 39 when he played 3 games at the position in 1946. 

Willy Mo Pena struck out in 21 consecutive games while playing center field. His streak ran from 5/19/2006 through 6/17/2007. In 74 at bats, he struck out an impressive 34 times.

Pena shattered the old record that was formerly held by Tony Armas and Billy Conigliaro. Their record was nine straight games.

Mike Timlin owns the Red Sox record for the most relief appearances in a season. He made 81 relief appearances in 2005.

Carlton Fisk owns the Red Sox record for most home runs hit in a season by a catcher. He hit 26 home runs twice—in 1977 and 1973.

David Ortiz had 119 bases on balls in 2006, good for the club record. In that same year, Manny had 100 bases on balls.

In 1957, Ted Williams hit 38 home runs at the age of 38. 

On 6/18/1975 at Detroit, Fred Lynn had 16 total bases. He went 5 for 6 that night, with 3 homeruns, 4 runs scored, and 10 RBI. The Red Sox won the game by a score of 15-1.

In 2000, Pedro Martinez had a K/BB ratio of 8.88 over 217 innings. 

Cliff Floyd had 28 extra base hits in only 171 at bats in 2002, setting the Red Sox season record for extra base hits with less than 200 at bats.

The Red Sox struck out 20 times in a game on two occasions, the latest being 6/5/2001 vs. the Tigers.

The Red Sox won in the bottom of the 18th inning by a score of 4-3.

Tim Wakefield allowed 6 homeruns on 8/8/2004 vs. the Tigers. He somehow earned the win, as the Red Sox won 11-9. 

Oldest player to have a season OPS above 1.000

In 1960, Ted Williams posted an OPS of 1.096. He was 41 years old.

note: For the sake of sample size, I only included batters with more than 200 at bats in my query. Williams had 310.