Strahm was 0-1 with a 2.61 ERA in 19 appearances in the pandemic-shortened 2020 season, in which the Padres ended a 14-year playoff drought. They beat St. Louis in the wild-card round before being swept in the NL Division Series by the eventual World Series champion Los Angeles Dodgers.
Pham, whose regular season was interrupted by a hand injury, hit .211 with three homers. He was stabbed outside a San Diego gentlemen's club in October and has sued the establishment.
Lamet, who became San Diego's best starter by going 3-1 with a 2.09 ERA, missed the playoffs with an elbow injury. Davies also is a starter while Altavilla and Pagan are relievers.
The Padres did not tender a contract to infielder Greg Garcia, who grew up in suburban El Cajon and is a grandson of the late Dave Garcia, who managed the Indians and Angels.