What is the final battle after the Millennium?
The final battle after the Millennium is the War of Gog and Magog, when Satan is released from the bottomless pit, deceives the nations into gathering against Jerusalem, and is destroyed by fire from heaven.
At the end of the thousand years, Satan is loosed out of his prison. He goes out to deceive the nations in the four corners of the earth, called Gog and Magog, and gathers them together for battle; their number is said to be as the sand of the sea. This is the final conflict that follows the Millennial Reign of Christ.
This army comes up on the breadth of the earth and surrounds the camp of the saints and the beloved city, Jerusalem. But fire comes down from God out of heaven and devours them, ending the battle immediately and completely. Scripture is careful to show that this is a distinct event from the earlier War of Armageddon, which took place before Christ's Millennial Kingdom was established. Ezekiel 38 describes this final Gog and Magog battle that occurs after the Millennium, while Ezekiel 39 describes the earlier War of Armageddon in which Gog was also a participant, but before the thousand years began.
After this final battle is destroyed, the devil who deceived the nations is cast into the lake of fire and brimstone, joining the beast and the false prophet, where he is tormented day and night forever. This is followed by the Great White Throne Judgment, where the dead are judged according to what is written in the books, and then the Second Resurrection, the resurrection of the wicked. After all this comes eternity: a new heaven, a new earth, and the New Jerusalem coming down from God, where God himself dwells with his people forever.
The scriptures
And when the thousand years are expired, Satan shall be loosed out of his prison, And shall go out to deceive the nations which are in the four quarters of the earth, Gog and Magog, to gather them together to battle: the number of whom is as the sand of the sea. And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them. And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them. And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.
And I saw a new heaven and a new earth: for the first heaven and the first earth were passed away; and there was no more sea. And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband. And I heard a great voice out of heaven saying, Behold, the tabernacle of God is with men, and he will dwell with them, and they shall be his people, and God himself shall be with them, and be their God.
And it shall come to pass at the same time when Gog shall come against the land of Israel, saith the Lord GOD, that my fury shall come up in my face. For in my jealousy and in the fire of my wrath have I spoken, Surely in that day there shall be a great shaking in the land of Israel; So that the fishes of the sea, and the fowls of the heaven, and the beasts of the field, and all creeping things that creep upon the earth, and all the men that are upon the face of the earth, shall shake at my presence, and the mountains shall be thrown down, and the steep places shall fall, and every wall shall fall to the ground. And I will call for a sword against him throughout all my mountains, saith the Lord GOD: every man’s sword shall be against his brother. And I will plead against him with pestilence and with blood; and I will rain upon him, and upon his bands, and upon the many people that are with him, an overflowing rain, and great hailstones, fire, and brimstone. Thus will I magnify myself, and sanctify myself; and I will be known in the eyes of many nations, and they shall know that I am the LORD.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.