1. The leftover oil from one day of Chanukkah may be used to kindle the lights on the next night. But whatever oil is left over [in the lamps] after the eighth day is forbidden for any benefit, since it was designated for its mitzvah. It should therefore be burned separately and not used for any purpose whatsoever (Shulchan Aruch and Mishnah Berurah 677).
2. Some say that only the oil that was needed for the minimum requirement was designated for the mitzvah – that is, the oil that was needed to last half-an-hour [such as the lights were somehow extinguished within the half-hour] – but all the rest is permissible for use. Others say that all the oil left in the lamps becomes forbidden, unless the person made an explicit condition from the outset that whatever will be left after Chanukkah shall not be designated for the mitzvah (ibid.).
