Why does it say "Li Gil'ad"?
Sanhedrin 104b: (A Mishnah lists six Jews who have no share in the world to. Expounders say that even they come to the world to come 1 . "Li Gil'ad" refers to Achav, who died in Ramos Gil'ad. "Menasheh" refers to Menasheh. "Efrayim Ma'oz Roshi" refers to Yarav'am (from Shevet Efrayim). "Yehudah Mechokeki" refers to Achitofel, of Shevet Yehudah. "Mo'av Sir Rachtzi" refers to Geichazi, who was stricken with Tzara'as (for deceiving Na'aman after he Rochatz (washed, i.e. immersed) to be cured from Tzara'as). "Al Edom Ashlich Na'ali" refers to Do'eg ha'Edomi.
Rashi: I (David) will rule over Gil'ad.
Radak (from Pirkei d'R. Eliezer 17): When Hashem wants to gather the exiles, first He will gather Gil'ad, for Anshei Yavesh Gil'ad did Chesed to Sha'ul and his sons. Hashem said, I will pay their reward in the future, and gather Gil'ad first!
Malbim: Gil'ad, and Menasheh and Efrayim (mentioned after this) will gather to help me.
Margoliyos ha'Yam (18): There is no argument. All Jews come to the world to come; the Mishnah lists sinners who do not receive a share above what they merited.
Why does it say "Efrayim Ma'oz Roshi"?
Refer to 60:9:1:1.
Radak: Efrayim refers to [Malchus Efrayim, i.e.] all of Yisrael other than Yehudah. (Binyamin is considered part of Yehudah - PF. It seems that this is Radak's intent; 'Acher' means since. It cannot mean after; Yehudah is the only Shevet mentioned here after Efrayim!)
Malbim: Efrayim, together with Gil'ad, and Menasheh (mentioned after this) will gather to help me. "Ma'oz Roshi" refers to "Yehudah Mechokeki" written after this; all will join to David (from Yehudah) to fight in the army for him.
Why does it say "Yehudah Mechokeki"?
Rashi: They are my officers. Mechokek is an expression of authority; he makes laws, sends letters and commands - "Lo Yasur Shevet mi'Yhudah u'Mechokek mi'Bein Raglav" (Bereishis 49:10).
Radak: Mechokek is the king - "u'Mechokek mi'Bein Raglav" (Bereishis 49:10). Kingship is from Yehudah. Hashem made me king over all of Yisrael for their benefit; through me, He will save them from those who seek to devour them.