Most nuts are generally healthy. Studies show that, walnuts contain rich omega-3 fatty acids, while almonds, pecans, hazelnuts, macadamia nuts, and other nuts also appear to be healthy.
Peanuts technically belong to legume (like beans), but they also seem to be relatively healthy. As for coconut, it does not have any nuts nutrients. Instead, coconut contain high unhealthy saturated fat.
Nut oils contain omega-3 fatty acids and vitamin E, but they lack plant fiber. Walnut oil contain highest omega-3 fatty acids. Nut oils contain saturated fats and unsaturated fats. Nut oils also contain high calories, so using them should be in moderation.