Saga (the cafeteria) is a place where friends run into one another and chat. A saga hug is a hug in which one sees a friend sitting at a table. One approaches the table at which the friend is eating. The friend sees them and quickly tries to finish chewing so they can say hi. The friend, however, is not willing, or perhaps able, to stand and greet them with a normal hug. The result, an awkward side hug where one is standing and the friend is sitting. A saga hug. The friend's face ends up in one's stomach or chest area and observers as well as participants feel awkward and uncomfortable.
"OMG, that was such an awkward saga hug! "
"oh hey girl! come over here and give me a saga hug!"
"and then, he gave me a saga hug! so. weird."