It is preferable to use olive oil for lighting the Hanukah candles, because the Menorah in the Bet Ha’mikdash was kindled with olive oil. Since our lighting commemorates the miracle of the Menorah in the Bet Ha’mikdash, it is preferable to use olive oil, which is what was used in the Bet Ha’mikdash.
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) writes that olive oil that is very bitter may nevertheless be used for the Hanukah candle lighting. Even if it is too bitter to be suitable for human consumption, the oil may be used for the Hanukah lights, as long as there is no spiritual contamination (such as by having been left underneath a bed).
Recent and contemporary Poskim addressed the question of whether this ruling applies as well to olive oil which is labelled, “Not fit for human consumption.” Some Halachic authorities, including Rav Nissim Karelitz and Rav Haim Kanievsky, maintain that the Ben Ish Hai’s ruling applies even to this oil. One could have argued that the Ben Ish Hai referred only to olive which has a bitter taste that makes it undesirable for consumption, but which could, potentially, be consumed, as opposed to oil which is entirely inedible, and could be harmful if consumed. The aforementioned Poskim, however, among others, dismiss this distinction, and maintain that there is no difference between the different kinds of olive oil with respect to the Hanukah candle lighting, and even olive oil which is entirely unfit for human consumption is perfectly acceptable.
Rav Yosef Shalom Elyashiv (Israel, 1910-2012), however, disagreed. In his view, it is preferable to use olive oil that is edible, since in the Bet Ha’mikdash edible olive oil was used. (Rav Elyashiv’s ruling is cited in Ashreh Ha’ish, p. 239.)
We should note that it is unclear whether olive oil labelled “Not fit for human consumption” is truly inedible. Some have claimed that companies add this label to the bottles in order to exempt themselves from the higher tariffs that are applied to food products, but the oil is, in truth, edible.
As for the final Halacha, it is certainly acceptable to use such oil for Hanukah candle lighting, but it would be preferable, if possible, to use edible olive oil in order to perform the Misva at the highest standard according to all opinions.
(Based on Yalkut Yosef – Hanukah, p. 117)
Summary: It is preferable to light the Hanukah candles with olive oil. While any olive oil is perfectly acceptable, some Halachic authorities maintain that it is preferable to use edible olive oil.