The connection between the second half of this haftara and Parashat Vayeira seems clear and straightforward. The Shunamite's conception after many years of infertility parallels Sara's pregnancy and birth to Yitzchak, of which we read in Parashat Vayera. The relevance of the first incident to Parashat Vayeira, however, is far less obvious. How does the sudden regeneration of the poor widow's oil relate to any of the stories told in Parashat Vayeira?
The haftara for Parashat Vayeira is taken from the fourth chapter of Sefer Melakhim II, and contains two episodes involving the prophet Elisha. In the first incident, a widow's creditor threatens to take her two sons as slaves if she does not repay her debt. Elisha miraculously has the small amount of oil in her possession reproduce manifold (very reminiscent of the Chanukah miracle), enabling her to sell the oil and pay back her creditor. The second incident is the famous story of the barren Shunamite woman, who finally conceives after receiving the prophet Elisha's blessing. Later, the child dies and is brought back to life by the prophet.
The connection between the second half of this haftara and Parashat Vayeira seems clear and straightforward. The Shunamite's conception after many years of infertility parallels Sara's pregnancy and birth to Yitzchak, of which we read in Parashat Vayera. In fact, the wording of the prophet's promise to the Shunamite that she would bear a child strongly resembles the promise of the angel visiting in Avraham and Sara's tent (compare Bereishit 18:10 and Melakhim II 4:16; Bereishit 21:2 and Melakhim II 4:17). The relevance of the first incident to Parashat Vayeira, however, is far less obvious. How does the sudden regeneration of the poor widow's oil relate to any of the stories told in Parashat Vayeira?
Rav Mendel Hirsch, in his work on the haftarot, suggests that this story forms a contrasting parallel to the values embodied by Avraham Avinu in Parashat Vayeira. The kindness and generosity of Avraham stands in direct opposition to the situation described in the haftara, where a creditor is poised to take away a widow's sons as payment for his debt. What more, Chazal (in the Midrash Tanchuma) say that the creditor was none other than Yehoram, king of the Northern Kingdom. That a king would act in such a manner and implement such a law, reflects perhaps the furpoint of deterioration from the ideals of Avraham. Additionally, it appears from the narrative that no one came to assist the widow, despite the fact that her husband had been a prominent prophet. By establishing this chapter as the haftara for Parashat Vayeira, Chazal implicitly lament the fact that Avraham's descendants had fallen so far from the values of kindness and sensitivity that he embodied throughout his life.
We may, however, suggest a different approach, one which takes into account the relationship between this incident and preceding narrative in Sefer Melakhim II. The previous chapter tells of Benei Yisrael's crushing victory over the nation of Moav. The final verse of that chapter, a verse that ranks among the most ambiguous pieces of narrative in all of Tanakh, tells that the king of Moav, seeing his army routed by Benei Yisrael, publicly sacrifices his eldest son, an act which resulted in "great wrath" befalling Benei Yisrael. Without elaborating any further on what precisely happened, the verse simply states that Benei Yisrael picked up and returned to the Land of Israel. (We should note that according to the Radak, the king of Moav killed not his own son, but the son of the king of Edom.) One view among Chazal (in Masekhet Sanhedrin 39b) explains that the king of Moav sacrificed his son to God. As Rashi cites from the Midrash in his commentary to Sefer Melakhim, the king's advisors suggested that he "compete" with Avraham Avinu's offspring for God's favor. If Avraham's descendants earn God's help in the merit of akeidat Yitzchak, when Avraham was prepared to sacrifice his son for God, then he, the king of Moav, would actually go through with such a sacrifice, and thereby, he figured, earn divine assistance. His self-sacrifice to God, though grotesquely misguided, was sufficient to arouse God's anger against Am Yisrael, who at that point in their history had betrayed the Almighty and did not show devotion and a sense of sacrifice to Him.
Which brings us to the beginning of the haftara for Parashat Vayeira. The opening verse of the haftara describes the poor widow as the wife of one of the prophets. According to Chazal, her husband was none other than the famous prophet Ovadya, who risked his life and gave all his money to hide, protect, and feed the prophets when Queen Izevel launched her campaign to kill all the prophets in the Northern Kingdom (see Melakhim I 18:13). Ovadya had taken huge loans in order to feed the prophets fleeing from Izevel's executioners, and so when he died, his creditor claimed the two orphans in exchange for the money. Chazal comment, "If not for the merit of Ovadya's wife, Yisrael would have been destroyed at that time" (Midrash Tanchuma, Parashat Ki-Tisa). The Midrash explains that the previous chapter ends with "great wrath" befalling Benei Yisrael as a result of the Moavite king's sacrifice to God, and this chapter begins with the description of Ovadya's widow. Chazal infer from this juxtaposition that her merit saved Benei Yisrael from the "great wrath" brought upon them by the king of Moav. How did her merit save them?
Rav Yehuda Leib Ginsburg, in his work, "Musar Ha-nevi'im," explains that she saved Benei Yisrael through the merit of her self-sacrifice. She supported her husband's efforts to protect the pursued prophets, despite the impoverishment it brought the family. This merit counterbalanced the divine rage triggered by the sacrifice of the king of Moav, and thus saved not only herself and her family, but all of Benei Yisrael, as well.
Herein, perhaps, lies the connection between this story and Parashat Vayeira, which concludes with the story of akeidat Yitzchak, the ultimate example of sacrifice. Though clearly the Almighty has no interest in the sacrifice of children (see Masekhet Ta'anit 4a), Avraham's preparedness to go to such an extent embodies the concept of self-sacrifice, our willingness to give of ourselves for the Almighty. It is this sense of sacrifice on the part of Ovadya's widow that saved Benei Yisrael at that time, and for this reason, perhaps, we read of the miracle that happened to her on the Shabbat when we read the story of akeidat Yitzchak in Parashat Vayeira.