What war did Bnei Efrayim fight?
Rashi (from Sanhedrin 92b): They left Egypt early, before the Ketz (time for redemption); they trusted in their Gevurah and their arrows 1 . They fought Anshei Gas (Divrei ha'Yamim I, 7:21).
Radak: This was in the Midbar. Even though it is not mentioned in the Torah, it is mentioned in Divrei ha'Yamim (I, 7:21 - "va'Haragum Anshei Gas ha'Noladim ba'Aretz."). They descended 2 to take their flocks. Their father Efrayim mourned over them many days. It seems that 8,000 died, like I explained there. This was against Hashem's word; He said that they will be 40 years in the Midbar!
Radak citing Ibn Ezra: The verse discusses the destruction of Shilo 3 , which was in Efrayim's portion. Malbim - it begins telling how Hashem despised Shilo. In the days of Eli, Bnei Efrayim bore bows, and even so they fled in the war with Pelishtim.
Sanhedrin 92b: They erred about the Ketz. Radak - the coming verses prove that this was after Yetzi'as Mitzrayim!
I do not know why he says 'descended'. Eretz Yisrael is higher than other lands (Kidushin 69a). In Divrei ha'Yamim, he said 'they entered the land to take their flocks.' (PF)
Radak: This is difficult. Later, the Mizmor discusses Churban Shilo (verse 60) in [chronological] order, after they entered Eretz Yisrael! (Radak himself (verse 15) points out that the Mizmor is not in order! However, he says that this is because the order is clear from the Torah. - PF) Also, all of Yisrael were in that war, and not only Bnei Efrayim!
What is the meaning of "Romei"?
Rashi: They throw (shoot arrows via a bow). This is like "Ramah va'Yam" (Shemos 15:1). Radak - "Noshekei" and "Romei" are both Samuch. We find like this - "Chachmei Yo'atzei Pharaoh" (Yehoshua 19:11).
Why does it mention that they took bows?
Radak: They relied on their weapons, and not on Hashem.
What is the meaning of "Hafchu b'Yom Kerav"?
Rashi: They turned to flee on the day of battle - "va'Haragum Anshei Gas ha'Noladim ba'Aretz" (Divrei ha'Yamim I, 7:21).