The way Odisseus reacts to the sudden news of his journey to Hades is, in my opinion, typical of the Greek tragedy: an emphatic, uncontrolled, even exaggerated use of the body and then, when it’s time to speak, an absolut control of the words: because the fate has been already set for them, the reaction of the body is something human (almost a “right” they have in bad destiny) but the speach to the gods has to be more “cold”, rational and, in this case, “practical”. This double reaction comes from the knowledge they cannot change anything in their lives; double reaction that doesn’t exist, for example, in the Italian tragedy of the Renaissance, also because of a different social and religous environment (Christianism).
I might add that this reaction (rolling on the ground, weeping) is also quite epic (consider Menelaus’ reaction to the knowledge that Nereus imparts to him concerning Agamemnon’s death)–even formulaic. Perhaps it would be interesting to compare Menenaus’ and Odysseus’ reactions closely (Tues.?).
Your point about the tragic reaction is a good one, but are you thinking about a specific text? A specific character? There are (especially female) tragic characters who do add language to their physical laments (Andromache; Cassandra; Hecuba, for example).
Nevertheless, I suspect you are hinting at what seems to be a constant theme running through Greek literature–a cosmic sense of pessimism.