Why does it say "Cherev la'Shem"?
Radak: The sword that will be among the Goyim - they will kill each other - it is for Hashem. He commanded and wanted this.
Malbim: This is vengeance against Edom for destroying His Kadosh Bayis.
Why does it say "Mele'ah Dam"?
Radak: This is from much killing. This is a metaphor, like "Ashkir Chitzai mi'Dam" (Devarim 32:42).
What is "Hudashnah"?
Radak: It is an expression of Dashen and fat; it became fat from Chelev of Karim (fat lambs). It is a composite of Pa'al and Hispa'el. It should be Hisdashnah.
What is the significance of "Karim Atudim"?
Rashi: They are officers and rulers.
Radak: This verse and the next mention goats, rams, Re'emim (giant animals), bulls and Abirim (fat or strong animals). This is a metaphor for Nochri kings, officers and viceroys.
What is the significance of "Chelev Kilyos Eilim"?
Malbim: This is not for vengeance, only for pleasure. The kidneys counsel for evil; He will return them to true Emunah.
What is the significance of Batzrah?
Rashi citing Pesikta: It is from Eretz Mo'av. However, since they established a king for Edom - "va'Yamas Bala va'Yimloch Tachtav Yovav Ben Zerach mi'Batzrah" (Bereishis 36:33), it will be stricken with them.
Radak (1): It says Batzrah, for it was a great city (even though this was not the place of the Zevach).
Malbim: Refer to 34:5:3:3. [The sword] will come to Batzrah for Emunah, so they will recognize Kel - "Mi Zeh Ba me'Edom Chamutz Begadim mi'Batzrah Zeh Hadur bi'Lvusho" (63:1).
Why does it say "Zevach la'Shem b'Vatzrah v'Tevach Gadol b'Eretz Edom"?
Malbim: The Zevach is for eating; there is pleasure from nullifying perverse mindsets and to 'arrange a table' of Emunah and Chachmah. The Tevach is for vengeance.