Why does the Torah need to tell us that Amram married Yocheved, and that Aharon married Elisheva bas Aminadav (6:23)?
Ramban #1 (to 6:23): It mentions the name of the mother of the prophets (Moshe and Aharon) in their honor; 1 and the mother of the kings, to teach us that she was a Meyucheses, from the family of kings, the sister of the celebrated Nachshon.
Seforno: To teach us why he merited to father the leaders of the generation from whom the Kohanim would ultimately be chosen. 2
Targum Yonasan: Refer to 6:16:2:4.
Baba Basra 109b: To teach us that one should always marry the daughter of 'a good person.' Moshe, who married the daughter of Yisro, 3 had a grandson called Yonasan (who worshipped Avodah Zarah); whereas Aharon who married the daughter of Aminadav, had a grandson called Pinchas.
Ramban: And to teach us that she was the daughter of Levi the Tzadik, hinting that a miracle was performed with her - that she bore children at the age of a hundred and thirty.
Seforno: And it is for the same reason that the Torah tells us that Elazar married a daughter of Puti'el, who was a leader of his generation (refer to 6:25:1:1). (Presumably, it is for the same reason that the Torah tells us that Amram married Yocheved - though it is unclear as to why the Seforno fails to mention it.)
While he was still a priest to Avodah Zarah.
How could Amram marry his aunt? According to Rebbi Eliezer (Sanhedrin 58a), an aunt is forbidden even to Bnei Noach!
Sanhedrin 58b: Yocheved and Amram's father Kehas, shared only the same father (Levi), but not the same mother. For Bnei Noach, Arayos based upon siblings are defined as those from the same mother. 1
This implies that Yisrael before Matan Torah had the Din of Bnei Noach. See also Torah Temimah, note 13.
How did Amram marry his aunt- a relationship that the Torah would later forbid to Bnei Yisrael?
Ramban (to Bereishis 26:5): Refer to Bereishis 26:5:3:1.
Gur Aryeh (to Bereishis 46:10): Refer to Bereishis 46:10:151.1 and Bereishis 46:10:151.2.
Why did it come about that Amram married his aunt, in order to produce Moshe?
Maharal (Gevuros Hashem, beg. Ch. 31, p. 119): That way, both Moshe's father and mother 1 would be from the Tribe of Levi, the tribe pre-destined to produce the redeemer. 2
But wouldn't the same be accomplished by Amram marrying any relative from the Tribe of Levi, such as his cousin or niece - relationships which the Torah would permit? Perhaps it is because a woman of a subsequent generation would not be purely from the tribe of Levi, as her own mother would have been from a different tribe. (CS) Regarding the critical importance of the mother in first establishing the Tribes, refer to Bereishis 37:35:1.1.
Refer to 6:14:1.1:1 and its note.
How can the sequence of Moshe's genealogy - Levi, Kehas, Amram, Moshe - be explained conceptually?
Maharal (Gevuros Hashem, beg. Ch. 31, p. 119): The ancestry of the redeemer developed in a specific order. Levi was a third-born; the significance of the number 3 was discussed above (see 6:14:1.1 and its notes). Since Levi was a 3, it was sufficient that his son Kehas be a 2, and Amram was a 1 (i.e. a firstborn) - as this would hasten the Redemption as much as possible. Moshe, the redeemer himself, had to be a third-born, due to the significance of 3.
QUESTIONS ON RASHI
Rashi writes: "'[Amram took] Yocheved, his aunt (Dodaso)' - [I.e., as Targum translates,] his father's sister. [Yocheved was] the daughter of Levi, and sister of [Amram's father] Kehas." Isn't this obvious?
Gur Aryeh: In other contexts, the term 'Dodah' refers specifically to one's father's brother's wife (see Vayikra 18:14). Rashi must therefore explain that here, it means his father's sister.