sayanora: Good-bye (like you didn't know that already!)
shojo-ai: Same thing as shounen-ai, but with girls.
shounen-ai: Yaoi's little brother. Shounen-ai refers to the emotional side of a male/male homosexual relationship. Usually in a shounen-ai story there is nothing past kissing.
yaoi: Commonly, yaoi is used to refer to male/male relationships (that is, homosexual relationships between two guys) in anime. Sometimes it is used to refer to the physical side of male/male relationships in anime. If that's the case, then yaoi's little brother is shounen-ai. Outside of anime, yaoi is known as slash.
yuri: Same thing as yaoi, except with girls. The non-anime version of yuri is, I think, fem-slash, or something like that.