It is forbidden to apply oil or cream [on Tish’a B’Av] even to a small area of the body. One is also forbidden to use cosmetics, like powders or salves, to beautify the skin or provide a nice fragrance. This prohibition applies specifically to anointing for the sake of pleasure; applying creams for medicinal purposes, however, is permitted. Therefore, one may apply Vaseline to dry lips or put on an anti-itch cream (Sh.A. 554:15). One may, similarly, put on mosquito repellant.
One may not smell spices on Tish’a B’Av, because doing so is pleasurable and one should curtail one’s pursuit of pleasures on the day on which our Holy Temple was destroyed. Granted, there are [halachic authorities] who rule leniently [on this issue] because [smelling fragrances] is not one of the five prohibitions (M.A.); nonetheless, most poskim hold that one should act strictly on Tish’a B’Av (Sh.A. 559:7, Sha’ar HaTziyun 556:1). See the footnote regarding smoking.
The Bi’ur Halachah (554:15) explains that there is a distinction between Yom Kippur and Tish’a B’Av regarding the prohibition of anointing. On Yom Kippur, the prohibition also includes non-pleasurable anointing, as the Yerushalmi indicates. Therefore, one may not apply, on Yom Kippur, a salve for the purpose of removing filth. On Tish’a B’Av, however, the prohibition is a function of the laws of mourning. Therefore, only anointing for the sake of pleasure is prohibited, while anointing in order to remove filth is permissible. The Bi’ur Halachah thus rejects the opinion of the Mateh Yehudah, who equates Tish’a B’Av and Yom Kippur in regard to this prohibition.
The author of Shiyurei Knesset HaGedolah (551, 567) writes that it is forbidden to smoke on fast days, because smoking alleviates the anxiety of the churban and generates a feeling of satiation; it even causes a desecration of God’s name, for the Gentiles refrain from smoking on their fast days. According to many [other poskim], however, there is no prohibition against smoking, from the perspective of the fast day, especially for someone who needs it to relieve agitation. The Mishnah Berurah (555:8) permits smoking after midday, in private, for one who needs it. Many others allow it even before midday, in private, for one who needs it. [R. Ovadyah Yosef] cites [these poskim] in Yabi’a Omer 1:33. The author of Hilchot Chag BeChag (7:87) writes that the authorities who forbid smoking are not referring to cigarettes, but to a type of smoking that entails more pleasure and involvement; see there. However, now that it has become clear that smoking is detrimental to a person’s health, it is forbidden to accustom oneself to smoking, and one who is already addicted must do everything he can to quit.