GrOGRE Ogre Chief
Greem Ogres will appear alone, with Ogres, or with Wizard Ogres and Hyenas. They're found in the beginning and middle of the game.
Being a member of the Giant category, the Giant Sword is more effective (in the WSC version).
Green Ogres are called Ogre Chiefs in the Japanese version and Ogre Chieftains in FF Origins. The idea comes from Dungeons & Dragons, which describes Ogre Chieftains, who are the strongest and smartest of their tribes. Ogre Chiefs return in FF2. For more ogre info see the Ogre page.