I have to confess that I read Obadiah and left with a lot of confusion. To help gain some understanding, I looked up some information on the book that I found to be pretty helpful, so I'm going to post it here. The text I am reproducing here comes from the ESV Classic Reference Bible. I hope you find this as useful as I did.
Obadiah wrote this shortest book of the Old Testament probably soon after 586 b.c. when the armies of Babylon destroyed Jerusalem. During this conquest, the people of Edom helped capture fleeing Israelites and turn them over to the Babylonians. They even took up residence in some Judean villages. This angered the Lord, for the Edomites, as descendants of Esau, were related to the Israelites (Gen. 25:21–26, 30) and therefore should have helped them. Obadiah prophesied that Edom would be repaid for mistreating God’s people. Within a hundred years, Edom was in ruins. Obadiah also asserted that God is sovereign over the nations and that the house of Jacob would be restored because of God’s covenant love for his people.