Why should Hashem rise in anger?
Rashi: He should be angry at my haters - Yishbi, his brothers (also giants) and Pelishtim, lest I be handed over to them.
Radak: Be angry at those who pursue me to kill me.
Malbim: It is as if the enemy is Hashem's staff to punish David. Rise in Your anger against my sins, and bear more anger against Tzorerai.
What is the meaning of "Hinasei b'Avros Tzorerai"?
Rashi: Glorify Yourself to show vengeance of Your anger against them.
Radak: With the anger that my afflicters have against me, rise against them and save me from them.
Why did he change from "Af" to "Evrah"?
Malbim: Evrah is when anger passed the limit of what is proper for the sin. Tzorerai are more angry than is proper, and prosecute to punish me more than is proper. You should have Evrah against them. Against me, punish me b'Af (like I deserve for my sin), like the verse concludes "v'Urah Elai Mishpat."
What is the meaning of "v'Urah Elai Mishpat"?
Rashi (from Shocher Tov 11): Enable me to do justice - the vengeance that You commanded - "Tero'em b'Shevet Barzel" (2:9), "v'Oyavti Es Oyvecha" (Shemos 23:22).
Radak: Arouse to me the Mishpat that You said is proper for me, i.e. kingship.