These are the correct terms for Australia:
Fizzy (carbonated) drinks are called 'soft drink', or 'fizzy drink' as a general term. 'Fizzy drink' is a bit childish though.
Coca Cola's flagship drink-flavoured syrup dilute is called "Coke" for short.
"Soda" refers to soda water, which is just carbonated water.
Edit: while we're at it, you generally ask for a specific drink by brand name, "Sprite", "Solo", "Coke Zero" etc..