さようなら /sayounara/ is more formal than じゃあ、またね /jaa, mata ne/ below and is used when you don't see that person again for a while. If you know you see him/her every day, use じゃあ、また /jaa, mata/ or じゃあ、またね /jaa, mata ne/.
2.
しつれいします /shitsuree-shimasu/ is formal and very polite. It literally means I will commit rudeness (by leaving). This is typically spoken by a younger/lower-ranking person (e.g., student) to an older/higher-ranking person (e.g, teacher).
3.
おつかれさま /Otsukare-sama/ literally refers to "your state of being tired." It is often used as a casual form of good-bye that also expresses appreciation for listener's effort. It can also be used for saying "Good job!"