Does having a little olive oil in one's hair prevent the water from reaching the hair and thus make wudoo’ invalid?.
It seems that the small amount of olive oil mentioned would not prevent the water from reaching the hair.
The basic principle, as mentioned by Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) is that if a person uses dihn (cream or oil) on the parts of the body washed during wudoo’, the dihn either remains solid, in which case it must be removed before doing wudoo’, because if the dihn remains solid, then it prevents the water from reaching the skin, and in that case wudoo’ is not valid.
But if the dihn is not solid, rather its trace is left on the part of body washed during wudoo’, then it does not matter. But in this case the person should make sure that he passes his hand over the part of the body in question, because usually the dihn repels water, so the water may not reach all areas of the part of the body being washed.
Fataawa al-Tahaarah, p. 147.
It may be added that the matter is less crucial with regard to the head because the obligation with regard to the head is to wipe it, not wash it, and wiping means that it is not essential for the water to reach every single hair.
Shaykh Ibn ‘Uthaymeen was also asked:
If a woman applies henna to her hair and it dries, and the like, can she wipe over it?
If a woman has applied henna to her hair and it has dried, then she may wipe over it and there is no need for her to undo her hair and wash off this henna, because it was proven that the Prophet had applied something to his hair to keep it together and prevent it from getting dusty whilst in ihraam, and what is applied to the hair is regarded as part of it. This indicates that there is some leeway with regard to purification of the head.
Fataawa al-Mar’ah al-Muslimah, 1/28.