Nutty Goodness Walnuts are an excellent source of omega-3 fatty acids, which protect the heart and ward off hypertension.They are high in antioxidants, which can lower the risk of coronary heart disease.Walnut- rich diets have been shown to lower cholesterol levels.By the handful…and more.Eat them freshly shelled or add them to salads, breads or yogurt. Walnuts are also tasty with apples and cheese.Add them to sautéed vegetables or to stuffing for turkey or poultry.