Why did she go to tell Elisha?
Rashi (citing Bereishis Rabah 35:3): She asked if she should sell the oil [now], or wait until the price rises more.
Radak citing Targum of Tosefta: She asked him whether she must tithe the oil. He told her, your husband fed Nevi'ei Hashem with a matter 'd'Leika Alei Isura' (tithes do not apply to it) 1 , also you need not tithe the oil, for it is miraculous 2 .
Why did it not need to be tithed? Revid Yosef (Chayei Sarah) says that Ovadyah bought Demai (one may feed it to Aniyim without tithing it), or it was exempt due to Piku'ach Nefesh. (I would not call that 'd'Leika Alei Isura'! Also, it is not related to the reason to exempt the oil! Rather, what he fed them was exempt mid'Oraisa due to (Devarim 14:22) '"Tevu'as Zar'echa", but not what you buy' (Bava Metzi'a 88b. Perhaps even the Chiyuv mid'Rabanan was not yet enacted.) Also the miraculous extra oil is not "Tevu'as Zar'echa", i.e. from your harvest! - PF)
Ohr Somayach (Hilchos Me'ilah 5:6, Hosafos): Ma'aser does not apply to increase via a miracle. Rinas Yitzchak (Melachim I, 17:13) - she was exempt because the oil that increased was already tithed. Eliyahu told the widow to separate Chalah from her dough that was blessed, because she had not separated Chalah before, since it was less than the Shi'ur for Chalah. (This is his intent; 'Ma'aser' is a printing mistake. - PF)
What is the meaning of "v'At u'Vanayich Sichyi ba'Nosar"?
Rashi citing Bereishis Rabah 35:3: The remainder [after paying the debt] is enough to finance you and your sons until Techiyas ha'Mesim.
Malbim: What remains in the flask will constantly flow with oil 1 to finance all your needs.
This seems unlike Malbim wrote above (verse 4) that if she moves, the 'spring' will be ruined, so she had to hold the flask titled until the miracle finished! (PF)
