Applying oil to the hair and keeping it clean is a Sunnah of the Prophet SAW. However, there is no specific "masnoon" method of applying oil to the hair mentioned in Sahih hadiths. Therefore, one should keep their hair clean and apply oil with the intention of following the Sunnah. Also, it is better to begin from the right side when applying oil or combing the hair, as the Prophet SAW preferred to initiate every good deed from the right side. In summary, it is not correct to deem one specific method as the "masnoon" way of applying oil.
Regarding applying kohl, the Sunnah of the Prophet (peace be upon him) is narrated through Ibn Abbas (may Allah be pleased with him). It is mentioned in a hadith from Tirmidhi that Ibn Abbas said: "The Messenger of Allah (peace be upon him) said, 'Apply "Asmad" (Antimony - a type of Kohl/Kajl) to the eyes, for it sharpens the eyesight and enhances the growth of the eyelashes.'"
Ibn Abbas also mentioned: "The Messenger of Allah (peace be upon him) had a kohl container, from which he applied kohl/kajl to each eye three times every night." (first three times in the right eye, then three times in the left eye).