My understanding is generally since the tax rates are higher in Australia, you'll likely pay extra Aus tax on any USD earned, but no US tax on AUD earned. I've seen some finance firms that specialize in this listed in the FB groups, but that's the extend of my knowledge about it. I'm sure someone will chime in with more accurate information.
Be very careful as there are three levels of income tax you have to deal with in the US and then other things like they have simplified tax return systems that don't really allow large claims. They have Federal, State and Payroll taxes to your income which will be based on your domicile, some are quite high others low, just like their GST system. You then have to fund your own medical unless its included in the package and 401k (super) which is employee contributions which may be matched by some companies to boost its value, again read the package. Many other small things that you have to pay for that are a given in Australia, other things are much cheaper.
If you go the the States and remain an Australian resident for taxation are you taxed on income streams in Australia by the IRS?
Pretty sure you only have to pay the Australian taxes, however the downside is that the Australian tax system will probably want its paws on anything you earn in the US as it finds its way back into Australia. That is if you are an Australian for tax purposes that means wherever you earn the money you pay Australian taxes as it comes back to the country. However already paid taxes to the IRS is most likely taken into account. The main issue is if you live in very low tax areas like the middle east, then the ATO will be taking a chunk as the money comes home.
Every year if you are an Australian citizen for tax purposes you will have to declare all income earned, even overseas for your tax return. That's when it gets messy.
From the ATO;
Your foreign income could be subject to double taxation if tax is withheld in the source country. To overcome this, Australia has a system of credits and exemptions and has signed tax treaties with more than 40 countries. This includes all our major trade and investment partners.