What is "Ge'ar"?
Pesachim 118b: It is rebuke. In the future, Malchus Romi will see that Mashi'ach accepts gifts from Egypt and Kush. They will think that all the more so he will accept from them, for they are our brothers! Hashem will tell Gavriel to rebuke them (Mashi'ach will not accept from them).
Radak #1: It is destruction. The same applies to "Ga'arta Goyim Ibadta Rasha" (9:6). Ge'ar is Makor (like an infinitive), like "Shechav ha'Melech" (Melachim II, 14:22).
Radak #2: It is a command, as if it had the prefix Tov. Also "Sim Kanecha" (Ovadyah 1:4) is like Tasim Kanecha. The kings will bring gifts to You when You will destroy Chayas (the congregation of, like I explained above, verse 11) Kaneh (the spear), i.e. those who fight with spears.
Malbim: [To'i, Melech Chamas,] sent to you (David) a gift, in order that You will confront Chayas Kaneh 1 and Adas Abirim b'Eglei Amim. I.e. David conquered To'i's enemies, who were like reed Chayos that tear, and the congregation of Abirim that gore with their horns.
This implies that he gives the gift to induce David to fight To'i's enemy. Malbim also says that it is because David already struck Hadad'ezer! This requires investigation. (PF)
What is "Chayas Kaneh"?
Pesachim 118b #1: It is Romi (Edom), which lives among Kanim (reeds) - "Yecharsemenah Chazir mi'Ya'ar v'Ziz Sadai Yir'enah" (80:14).
Pesachim 118b #2: It is a nation (Edom) that all of its decrees are written with one quill (all are directed against Yisrael).
Some texts of Rashi: It is Amalek. (Other texts say Esav, like Pesachim 118b - refer to 68:31:2:1.)
What is "Adas Abirim b'Eglei Amim"?
Pesachim 118b: [Edom slaughtered] the congregation of mighty ones like calves of Amim (everyone, i.e. Hefker).
Rashi: A nation that grew fat, and became like mighty bulls amidst the other nations, which are like calves compared to them.
Radak: The congregation of mighty ones came upon Eglei Amim (the kings and officers 1 ) and destroyed them, until the remnant appeases You with pieces of silver.
Radak: They are compared to calves - "Sevavuni Parim Rabim" (22:13). (There, they are compared to bulls! Perhaps Radak merely means that they are compared to cattle. - PF)
What is the meaning of "Misrapes b'Ratzei Chasef"?
Pesachim 118b: They are Matir Pas (open their hands) to take money, and do not fulfill the deal [for which they took tribute].
Rashi: They are not pleased with anyone, unless he appeases them with coins.
Radak: They bow [and give silver, to appease]; this is like "Hisrapes u'Rhav Re'echa" (Mishlei 6:3).
Malbim: To'i bowed and humbled himself in front of you with money that he took as spoils from nations that desire war.
What is the meaning of "Bizer Amim"?
Pesachim 118b: What caused Yisrael to be Mefuzar (scattered) among the nations? "Keravos Yechpatzu" (Yisrael desired closeness with them).
Rashi: They scattered the Shevatim. [The Shevatim are called Amim,] like "Af Chovev Amim" (Devarim 33:3).
Radak: Hashem scattered the nations "that wanted to fight us." "Bizer" is like Pizer. Also "u'Rechush Lahem Yivzor" (Daniel 11:24) is like Yefazer. Beis and Pei are pronounced from the same place (the lips, so they are interchangeable).
Why does it say "Keravos Yechpatzu"?
Pesachim 118b: Refer to 68:31:5:1.
Rashi: They always seek to fight us.