When we call a country oil-rich, we mean there is a lot of oil under its land or under the sea beside it, and that oil brings in a lot of money. You will hear this in news English far more than at the dinner table: an oil-rich country, an oil-rich region, an oil-rich state. Though actually, the place is not oily to touch. The 'rich' is the oil in the ground, and the money that follows. People sometimes stretch the same pattern to food — oil-rich fish, oil-rich seeds — meaning the food itself holds a lot of oil. That is a different picture, so keep the country sense and the food sense apart.