What did Yaakov mean when he said to Esav, "Swear to me ka'Yom..."?
Refer to 25:33:2.
Interestingly, Targum Yonasan learns here like Rashi and Targum Onkelos to 25:31.
Why was the oath necessary?
Seforno: Since the acquisition concerned something abstract 1 that cannot be acquired through the normal channels, the oath made up for the deficiency.
Ramban: When Esav rejected the Bechorah, Yaakov asked him to swear that his rejection was permanent (that he would never ask for it), and Esav complied.
Rivash (328, cited in Ohr ha'Chayim): The Shevu'ah was superfluous, to dissuade the strongarm Esav from disputing his sale later.
Ha'amek Davar, Harchev Davar: It was lest Esav retract. The sale was invalid, for it was Davar she'Lo Ba l'Olam. 2
How was the transaction performed from a legal point of view?
Seforno: The lentil stew acted as a Kinyan Chalipin, in exchange for which Yaakov acquired the Bechorah, and Yaakov remained obligated to pay, at a later date, the sum that they agreed upon.
Ramban: Refer to 25:31:2:2.
Rashbam: Yaakov paid money for the value of inheriting an extra portion. The food was like the custom of buyers and sellers to spend a coin or two on wine [and drink it].
What was Yaakov's Heter to swindle Esav?
Moshav Zekenim #1, Da'as Zekenim: We learn from here that if a Rasha has a Sefer Torah or other Mitzvah, one may take it from him through deception.
Moshav Zekenim #2, Hadar Zekenim: Esav was close to death. Yaakov said, I do not want to give to you; you will die, and I will inherit everything. I give only if you sell your Bechorah, so I will not lose. The sale was valid, for also without the sale, Esav would have died and Yaakov would have become the Bechor. 1
Ohr ha'Chayim (citing Maharik CM 227): If one sold for less than the value because he was in great need (e.g. of money), the sale is valid. Esav knew, and pardoned (being underpaid).
Yevamos (106b, according to the Ramban): If one stipulated to pay someone a great sum to save his life, he gets only his normal wage, for he was obligated to save him! Perhaps Yaakov recognized that there is no Mitzvah to save Esav's life; Gitin 47a says so about a wanton sinner. (PF)
The Bechorah includes Devarim she'Lo Ba'u l'Olam (matters not yet in the world). Chachamim hold that such matters cannot be sold; why was the sale valid?
Rivash (328, cited in Ohr ha'Chayim): Before Matan Torah, one could be Makneh Davar she'Lo Ba l'Olam.
Ha'amek Davar, Harchev Davar: Indeed, the sale was invalid. However, according to R. Tam, 1 it is valid until he retracts. 2 Due to the Shevu'ah, Esav would not retract. Also Malbim implies like this.
Moshav Zekenim: Esav sold only what (i.e. if) he will inherit that day, which takes effect, 3 and afterwards it endured automatically.
Harchev Davar: The Rosh holds that the sale is totally invalid. He must hold like Rivash (refer to 25:33:152:1). Rivash - the Tur and Rosh would not learn from here that with a Shevu'ah, such a sale takes effect. This is unreasonable. Also, we cannot bring a proof from before Matan Torah!
The Rema (CM 209:4) says like this. (Harchev Davar cited other places in Shulchan Aruch, but they do not seem to discuss this - PF.)
Bava Metzia 16a. Ohr ha'Chayim - an enactment allows an Ani to sell what he will inherit or earn in one day, so he can receive what he needs for today. The sale was based on this. Esav was about to die, so surely the enactment applies!
Why did Yaakov say, "swear to me"?
Ohr ha'Chayim #1: The Shevu'ah is based on my intent; so you cannot nullify it in your heart.
Ohr ha'Chayim #2: The Shevu'ah was to uphold the sale. Sale of a Bechorah can only be to me (i.e. another son).