Why does it mention Edom now?
Radak: Edom is Se'ir, which was mentioned above with Mo'av (8).
What vengeance did Edom take against Yehudah?
Radak: They showed vengeance, even though Yisrael did not sin against them, and did to Yisrael what they did, like it says in Ovadyah (1:14) "v'Al Ta'amod Al ha'Perek Lehachris Es Pelitav."
Malbim: Edom harmed Yisrael in the first Churban in the way of vengeance - "Ya'an Heyos Lecha Eivas Olam va'Tagar Es Bnei Yisrael Al Yedei Cherev" (35:5).
What was their sin?
Radak: They sinned against them, for they are their brothers. They did not remember the Bris of brothers.
Malbim: In Bayis Sheni when Edom came to do Bris Milah and converted via the Chashmona'im kings, and after the Romans came to destroy Yerushalayim, they were guilty and transgressed the Bris and took vengeance against them. This includes their vengeance at the time of Galus, through Shemados (decrees against Mitzvos) and eradicating [Yisrael].
