I finally found a cleansing oil I like as much as the DHC olive oil cleanser I tried in Japan. It's the Origins Clean Energy cleanser.
The oil is great at removing dirt and the cleanser also contains emulsifiers that react with water so it rinses off easily. This is a blend of different oils (olive, sesame, sunflower, etc.) and no parabens, artificial colours or perfumes. That cheery yellow colour is all natural!