What olive oil should be used for the Chanukah lighting?
[From the letter of the law] all oils may be used for the Chanukah candles. This applies even if the flame does not light well with the oil. Nevertheless, it is a Mitzvah Min Hamuvchar to use olive oil. If olive oil is not available, one is to use other oils that give a pure and clean flame.
One is to use olive oil. If olive oil is not available, one is to use other oils which give off a good flame, or use bees wax.
May one use olive oil that is not fit for eating?
Yes. However, some Poskim rule that it is best to use edible oil, for those who wish to follow the ruling of Mehadrin Min Hamihadrin. Accordingly, it is better [more Mehudar] to use regular olive oil that is fit for consumption during the year [virgin or extra virgin] than to use the olive oil that is marketed as “Shemen Lamaor,” or “olive oil for lighting”
Beware of fake olive oil:
Unfortunately, the olive oil market is flooded by fake and counterfeit olive oils that are sold for the price of olive oil [or slightly cheaper to create a bargain] when in truth they are made of other, cheaper oils with some flavor, color and other additives so it appears like olive oil. Due to this, various countries contain agencies who certify the authenticity of olive oil, and if one wants to make sure he has received a real product, one should check that the company has the certification tag. Unfortunately, from past experience, having a Hashgacha on the oil does not suffice as proof for its authenticity, despite their vouch for its status of Kashrus.
 Michaber 673:1; Shabbos 21b
The reason: The novelty of this ruling is that one would think that bad quality oils should not be used due to fear that the candle may extinguish prior to the half hour. The reason it is nevertheless permitted is because the law is that even if the candle extinguishes one still fulfills his obligation, as the lighting fulfills the Mitzvah. [M”B 673:1]
 Michaber ibid
 Rama ibid in name of Mordechai; Kol Bo and Maharil; Admur 264:12
 Rama ibid
 The difference between the oils: There are five gradations of olive oil, which are based on their level of acidity, and quality of press. Virgin, and extra virgin olive oil have a very small percentage of acidity, and come from the first press. Olive oil that is marketed as “for lighting purposes only” is of very low quality as it is not from the first press, contains a high percentage of acidity, and usually contains chemicals which help in its extraction.
 Ben Ish Chaiy Vayeishev 12 “However, if it is inedible due to bitterness, it is permitted.”; Kaf Hachaim 673:11; Piskeiy Teshuvos 673:5 All oils are valid for the Menorah lighting. [Michaber 673:1] The oils do not have to be fit to be eaten. [As proven from the lack of mention made in Shulchan Aruch and similarly that most Poskim agree one may light using Cheilev which is forbidden to eat due to being not Kosher].
 Rav Mordechai Eliyahu; Rav Yaakov Yosef; Yalkut Yosef Chanukah p. 117; Rav Elyashiv, brought in Ashrei Ish p. 239
 The reason: Some say that inedible oil should not be used for a Mitzvah as it is repulsive, and is similar to the prohibition against using oil that had a rat fall inside. [Rav Mordechai Eliyahu based on Rama Y.D. 104:2] Alternatively, since they add chemicals to the extraction process, therefore it is considered “Panim Chadashos” and is not considered olive oil at all, and is thus no better than any other oil on the market. [Rav Yaakov Yosef] Alternatively, edible oil that was used in the Mikdash, therefore, it should likewise be used for the Chanukah lighting. As well, the better the oil the more one beautifies the Mitzvah.
 Check out here for a list of certified authentic olive oils: http://blog.aboutoliveoil.org/21-olive-oil-brands-certified-for-authenticity
 See the following report on this issue: http://www.bhol.co.il/3820/%D7%9C%D7%90-%D7%A9%D7%9E%D7%9F-%D7%9C%D7%90-%D7%96%D7%99%D7%AA-.html