Australians use the same word as the rest of the English-speaking world: storm.
However, Australians might use "weather" as a more informal term for a storm, particularly if it's a severe or heavy storm. For example, "There's some crazy weather coming in tonight!".
They might also use more specific terms depending on the type of storm, like:
* "thunderstorm" for a storm with thunder and lightning
* "cyclone" for a tropical storm
* "bushfire" for a wildfire, which can be associated with dry storms
* "dust storm" for a storm with high winds and dust
Ultimately, Australians use the same vocabulary for storms as any other English speaker, but they might have a more relaxed and informal approach to describing them.