What are the two signs in "The Odyssey" sent from Olympus to indicate the gods' approval of Odysseus?just as the epic reaches its climax

I'm not quite sure where you're identifying the epic's climax, but here are some likely events.

In Book 20 when Odysseus asks Zeus to show him a sign, "a good omen voiced by someone awake indoors,/another sign, outside, from Zeus himself," Zeus immediately sends a clap of thunder out of a clear blue sky. A woman who has been grinding wheat interprets the thunder as a sign from Zeus, and she prays that the day may be the suitors' last.

In Book 21 after the Odysseus disguised as the old beggar has successfully strung the mighty bow, "Zeus cracked the sky with a bolt, his blazing sign," and Odysseus lets fly an arrow that shoots straight through all twelve axe-heads, thus completing the test of the bow.

In Book 22 during the battle with the suitors, twice Athena sends signs. Once when Agelaus commands six men to throw their spears at Odysseus at the same time, she sends all of the shots "wide of the mark"; nothing hits Odysseus. All of the spears land harmlessly. Then later Athena takes the form of her aegis, or shield, high in the rafters of the great hall and terrorizes the suitors who stampede like wild cattle in their panic until the floors run red with blood.