Flanagan, who joined the club in 2006, started 13 games at center last season and played in 14 overall. In two seasons with Houston, he played in 23 games, with 22 starts.
Barber played in six games before going on injured reserve with a neck injury Oct. 31. He had two tackles on defense and four on special teams in his one season with the team.
Putzier started one game at tight end in 2007 and saw action in eight others. He had six catches for 39 yards and a touchdown.
Hodgdon, the team's fifth-round pick in 2005, went through training camp but was released before the start of the season. He rejoined the team in December and played in two games.
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