Eucalyptus oil is an essential oil used as a remedy for various ailments and diseases including nasal congestion, asthma, and tick repellent. Eucalyptus oil can also be used on the skin as a remedy for health problems such as arthritis and skin ulcers. Eucalyptus essential oil can be used to relieve cough in a number of ways. One might want to try applying a few drops of eucalyptus oil to one ounce of carrier oil and rub the mixture into the chest and throat