Is Australia a Continent, an Island or both?

Continent.

Australia is the only country that is both a continent and a country (both sharing the same name).

Continents are typically very large land masses. Australia is the smallest continent. Islands are much smaller than continents. The largest island is Greenland.

The country of Australia includes the Australian continent, the island of Tasmania and other islands in the Indian, Southern and South Pacific Oceans.

Post Edit:

Answer slightly changed to reflect the completely changed question.

Yes, it is in Oceania.

A country which is in the continent of Oceania

Don't you know how to do a Google search? In Australia we are taught since baby's grade that we are an island, a continent and a country. Australia has an official international Country phone code "61", that makes us a country. We are officially the sixth continent in the world (Antarctica the 7th being the only one discovered after us), and we have sea/ocean all around us, which logically makes us an island.