The Collaborative International Dictionary of English v.0.48:

Stagy \Sta"gy\ (st[=a]"j[y^]), a. [Written also stagey.]
   Having an air or manner characteristic of the stage;
   theatrical; artificial; as, a stagy tone or bearing; --
   chiefly used depreciatively.
   [Webster 1913 Suppl.]

WordNet (r) 3.0 (2006):

stagy
    adj 1: having characteristics of the stage especially an
           artificial and mannered quality; "stagy heroics" [syn:
           stagy, stagey]

Moby Thesaurus II by Grady Ward, 1.0:

44 Moby Thesaurus words for "stagy":
   actor-proof, affected, all-star, artificial, ballet, balletic,
   cinematic, cinematographic, dramatic, dramatical, dramaturgic,
   film, filmic, ham, hammy, histrionic, insincere, la-di-da,
   legitimate, maniere, mannered, melodramatic, milked, monodramatic,
   movie, operatic, overacted, overdone, overplayed, pretentious,
   scenic, spectacular, stagelike, stageworthy, starstruck, stellar,
   theaterlike, theatrical, thespian, thrown away, underacted,
   underplayed, unnatural, vaudevillian