Radak: He will judge everyone correctly - poor and rich! The way of the world is to favor the Gedolim and rich. He will justly take for the poor what they deserve from the rich.

Malbim: Tzedek itself will help him to discern the verdict; he will not err due to the litigants' claims.

Rashi: It is a pleasant, soft expression.

Malbim: Straightness itself will help him to balance to rebuke the humble, who accept rebuke.

Radak: He will rebuke the strong, that they should not steal from the humble or oppress them, for they are weak. The prefix Lamed in "l'Anvei Aretz" is in place of Ba'avur (for the sake of), like the Lamed in "Imri Li Achi Hu" (Bereishis 20:13) and other verses.

Rashi citing Targum Yonasan: He will strike those of the land who are liable [through the words of his mouth].

Radak: [He will strike] the Resha'im. Because it mentioned the humble, it is understood that they are the opposite; it relies on [the reader] to understand. Also the end of the verse proves this - "Yamis Rasha." Also, it is understood that he will strike one who is proper to be hit, for it says "v'Hochi'ach b'Mishor l'Anvei Aretz." Refer to 11:4:5:2.

Malbim: If he will find a land that will not accept his words, he will strike them verbally, i.e. via a curse. He will not need a [physical] staff.

Rashi citing Targum Yonasan: And the words of his lips.

Radak: He will strike them verbally, i.e. via a curse, and they will die - "v'Sigzar Omer v'Yakam Lach" (Iyov 22:28). It says about Shmuel ha'Navi "Kol Asher Yedaber Bo Yavo" (Shmuel I, 9:6). Elisha cursed with Hashem's name, and two bears came from the forest, and killed 42 youths (Melachim II, 2:24).

Malbim: For an individual Rasha who rebels against him, he will not need to curse him. The Ru'ach that comes out of his lips will kill him. Normally, after one speaks, additional Ru'ach comes out of his lips. That will suffice to kill the individual Rasha, without speaking about him at all.