“Call” is when a member of the cast or crew is expected to be at the venue for the performance. Exactly when it is depends on specific details of the show and perfornance (Are there complicated costume requirements? Does the director want to do warm-ups? Is there a way to get backstage without being seen by the audience?) but is typically an hour or so before curtain.
Callbacks are a second round of auditions, held if directors decide they need to hear auditionees read additional material, or hear them in additional combinations (“How well would these two actors do in this particular scene?”, for instance). Callbacks are not always needed, and when they do happen, not being called back doesn’t mean you won’t (or will) be cast; it just means a director doesn’t need another reading from you in order to make a decision.
Foley effects (or just “Foley”) are sound effects produced by sound-effects artists (“Foley artists”) with equipment and materials on stage or in the studio, such as a door with locks, a wooden platform and hard-soled shoes, or a heavy chain in a metal mixing bowl (which makes a pretty good explosion sound). They’re distinguished from recorded or digitally generated sound effects. (They’re named after sound-effects artist Jack Foley.)
The green room is where the performers wait when they’re not on stage. It is rarely actually green and occasionally it’s not even a room. Both churches we regularly perform at have very nice green rooms.
“Sides” are lines of dialogue provided for an audition — typically, a selection of short extracts from the script to be performed, intended to provide a representative sample of the characters and emotions the directors are looking for.