Rashi: It was when Yehoram was ill in Yizre'el.

Rashi (from Seder Olam 18): It was Yonah ban Amitai.

Rashi: This is an expression of acting with zeal and Gevurah, for he was sent on a dangerous mission.

Radak: He should go quickly and return quickly, while Yehoram is not here; he was recovering in Yizre'el. It says "v'Nastah v'Lo Sechakeh" (verse 3).

Malbim: Run quickly, for now it is easy to seize power. Yehoram was ill in Yizre'el with no one to help him, for all of [the army of] Yisrael were in Ramos Gil'ad.

Radak (citing Horiyos 11b): It was due to the opposition of Yehoram ben Achav. He did not take Shemen ha'Mishchah; that is only for Malchei Beis David. Rather, it was Afarsimon oil. Malbim (2) - he wanted it to resemble anointment with Shemen ha'Mishchah.

Radak citing Megilah 14a: David and Shlomo were anointed with a horn ¹ (of oil), and their kingships lasted. Sha'ul and Yehu were anointed with flasks, and their kingships did not last.

Malbim: Elisha's request "vi'Yhi Na Pi Shenayim b'Ruchacha Elai" (2:9) was that two matters incumbent on Eliyahu, i.e. anointing Yehu and Chaza'el, Elisha will do them. Even though it is punishment, Elisha wanted to do so, to avenge the blood of Nevi'ei Hashem. Initially the decree was to do so in the lifetime of Achav's son; via Teshuvah, it was delayed.

Radak: Perhaps Yisrael were in a camp outside the city, intending to take it back; Melech Aram was in the city. Melech Yisrael was stricken there; he went to Yizre'el to recuperate, and left the camp there. The Shali'ach should anoint Yehu in the camp ¹ .

Radak: We must say that a Melech Yisrael took it afterwards - Yeho'achaz ² or Yehoram. Chaza'el went to take it, and Melech Yisrael went there with his camp.