How can I get a job in Australia, not being an Australian or even EU citizen?

It's definitely not impossible, Australia works on a points system for immigration - so it helps if you have a degree, if you're young and if you have a certain amount of money behind you. I'm no expert, but I'd advise logging onto an Australian immigration website to check it out.
If you want to stay for a short time, there's visa options - which vary greatly depending on where you're from.
Good luck!

For one thing, Australia isn't part of the EU..

But yeah I believe you don't have to be a citizen there to have a job. Most of their companies are American ones too.
Don't bother. Get a job in your own country.
you need a visa!! either contact the Australian embassy or your Embasy for where you are a citizen. You will need some cash behind you to enter though.
It is highly impossible