There are probably thousands of uses for Eucalyptus but I'll just mention a few of them here for you. The first would be mixing or blending Eucalyptus with other essential oils. Eucalyptus is a "Top Note" so it would blend well with a Base and Middle note. We all prefer certain scents so this is an area where experimentation is key.
Some common examples of Middle Notes: Geranium, Jasmine and Tea Tree. Common examples of Base Notes: Frankincense, Vanilla and Sandalwood. There are many more to choose from so be creative. When you come up with a winning combination of Eucalyptus and two other essential oil notes, then you can add that combination to your soap.
Eucalyptus essential oil by itself has a strong scent that is sharp on the nostrils! It is beneficial to the respiratory system. This is why your local health clubs use Eucalyptus in their steam rooms. Eucalyptus is a strong enough scent that it actually repels insects. I think Eucalyptus is a much better choice than purchasing and slathering on heavily concentrated amounts of deet which is in most commercial insect repellents.
Add a Eucalyptus soap bar in your dresser drawer and enjoy the refreshing mild scent it will leave on your undergarments. Finally, Eucalyptus may help with relaxation if you are in a rather stressful state.
If you're not familiar with the scent of Eucalyptus either purchase a small bottle of the essential oil or purchase Eucalyptus soap bars to enjoy the fragrance.