From Jason Hood
Psalm 81: The psalmist calls to raise the music in order to remind us of what God accomplished and what he deserves because of what he accomplished: he "removed the burdens" of his people and as a consequence calls them to listen to him and commit to exclusive worship of this one God. As our mouths open to sing his praises, they are filled with the goodness of God's word.
Psalm 82: "Gods" here probably refers to godlike rulers, "sons of God" in the ancient world. In contrast to the popular modern post-enlightenment conception of the world, God has an agenda for rulers to follow--and reminds us that no matter how powerful or satiated we are in this life, death (and judgment) comes for all. Those who are going to share God's inheritance (82:8) must share his character as they rule.
Psalm 83: An extended prayer featuring a careful counting of Israel's enemies. These enemies are enemies both of God and his people (vs 2-3). Somehow the psalmist is simultaneously praying for destruction/judgment as well as an awakening on the part of his enemies, that they would seek God's name and know that he alone is the Most High God.
Deuteronomy 9:9-21: Moses rehearses his mediatorial role for God's people, which reminds us of Jesus' even greater role in meditating between the judgment of God and his people, the lawless covenant breakers who don't even deserve to have the law, let alone the precious gift of a mediator who repairs the relationship between God and his people.