Oils and Fat
Depending on what you mean by oily, there are several answers.
Actually certain fatty foods are good for you like avocados, olive oil and coconut oil. Artificial oils are not so good. Deep fat frying, especially with animal lard, usually is not very good for you. The omega 3 fish oils, found in salmon and tuna, are good for you, but still don't eat these too frequently. Remember moderation!