What is the meaning of "Ki Rivesah va'Shamayim Charbi"?
Rashi: [My sword was satiated] to kill the Sarim above. Afterwards it will descend on Amalek. No nation is stricken below until its Sar above is stricken.
Radak: My sword in Shamayim will be satiated with the blood of these bodies. This is a metaphor, for decrees descend from Shamayim.
Malbim: The verse depicts Hashem's sword as an entity that tears, and eats the bodies of the killed and their fat.
Why does it say "Al Edom Tered... l'Mishpat"?
Malbim: Do not say that I will do so without Mishpat. After My sword will be satiated in Shamayim (against the Sarim, it will take vengeance without Mishpat), afterwards it will descend on Edom b'Mishpat - "v'Shafateti Oso" (Yechezkel 38:22). Edom is the known nation that serves idols and stars.
What is "Am Chermi"?
Rashi: The nation of My war. This is like it says 'our Mishnah was taught at a time of Cheirum' (Kesuvos 17b). Also "Es Ish Chermi" (Melachim I, 20:42, refers to war).
Radak: (On whom will this sword descend from Shamayim?) On the nation that I want to be Macharim, to judge them for doing evil to Yisrael.
Malbim: Batzrah was the primary city of Edom's Emunah. Their head priest dwelled there. It is Am Chermi - I have a quarrel of Emunah with them. I will come to Mishpat with Edom and Batzrah.
