If you're living in Australia for several years, you're a resident there. So you can apply for a visa from an Italian or (depending on your main destination) consulate in Australia.
There is no requirement that you travel directly to Australia after your trip. Really, what they want to know is just that you have a good reason to exit to somewhere that is not in the Schengen areal. Usually, the way you convince them of that is that you show documentation that you need to be back in Australia at a certain time to continue your studies, but nobody says you have to go there directly from Europe.
It can be difficult for students to show a good enough economy and ties to their country of residence to qualify for a visa, but you'll have a somewhat easier starting point than most because you already have legal residence in an affluent country, and therefore are less likely to want to immigrate illegally to a Schengen country.