Australia, along with every other country on Earth will hire American pilots as long as they meet the exact same requirements that American companies require from non-Americans.
1. The right to live and work in that country.
2. A license issued from that country.
As for obtaining a work visa, again, the requirements are no different than those required for non-Americans in the USA. If you weren't born in Australia, you pretty much have to marry an Australian. No different to US legal immigration requirements.
European requirements are the same, however certain Asian airlines will hire foreigners without local residency as professional guest workers, usually for a specified, but renewable time period.
Good luck, pprune is a better source of information on working outside the US than FI.