That's in addition to lefty reliever Brandon Sisk, acquired from the Royals in exchange for Ervin Santana, and infielder Angel Sanchez, who was signed before the end of the World Series.
The Angels also have 30-year-old right-handed reliever Tony Pena, whom they signed last season to a two-year Minor League contract. Pena, who posted a 4.43 ERA in 379 2/3 innings in the Majors from 2006-11, rehabbed from Tommy John surgery in the Angels system this past season and will join them again in 2013.
All of them have experience in the Majors and all will be invited to Spring Training camp, either to compete for a big league job or increase the organizational depth. As for Major League deals, the Angels' attention is solely turned towards pitching.
"Right now," general manager Jerry Dipoto said, "our primary focus is on pitching and we're very comfortable with the position-player club that we have."
Shuck and Oeltjen, both left-handed hitters who can play all three outfield spots, will likely compete with Kole Calhoun for the 25th roster spot this spring.
Shuck, 25, played in 37 games with the Astros in 2011 and hit .298 with 12 steals in their Triple-A squad in 2012. Oeltjen, 29, has played in 99 Major League games through three seasons and hit .294 with 13 homers and 61 RBIs with the Dodgers' Triple-A affiliate in 2012.
Harris, who will compete with Sanchez and Andrew Romine for the utility-infield spot vacated by Maicer Izturis, played for five different big league organizations from 2004-10. He was solid with the Rays in '07, batting .286 with 12 homers and 59 RBIs, and hit .317 with the Rockies' Triple-A affiliate this past season.
Reyes, 27, went 12-26 with a 6.05 ERA in 70 big league games (62 starts) from 2007-11, then posted a 2.51 ERA in 61 innings in the Pirates' system in 2012.
The 31-year-old Stetter posted a 4.08 ERA in 132 games with the Brewers from 2007-11 and had a 2.67 ERA in their Minor League system in 2012. Buckner had a 6.25 ERA in 36 games (21 starts) from 2007-10, then posted a 3.65 ERA in 27 starts in the Red Sox system in 2012.
Carlin, a 31-year-old switch-hitter, compiled 56 games in the big leagues from 2008-12 and spent the last two seasons playing mostly with the Indians' Triple-A affiliate, batting .252 in 62 games in 2012.
Alden Gonzalez is a reporter for MLB.com. Read his blog, Gonzo and "The Show", and follow him on Twitter @Alden_Gonzalez. This story was not subject to the approval of Major League Baseball or its clubs.