An informal reference to a resident of Australia is "Aussie," and an informal reference to the country itself is an even shorter derivative of the word, "Aus." When residents pronounce "Aus" with a hissing "s" sound, it sounds like "Oz," which has resulted in the country's informal nickname of "Oz."
Australia is also known as "The Land Down Under," a name given to the country by European explorers. The explorers had set sail in search of land under the continent of Asia, and what they found was Australia. Hence, its positioning in the southern hemisphere underneath Asia is the reason for this nickname. Another common nickname and informal reference for Australia is "The Outback."