If I have a call option, which I long, with a strike price say, AUD 1.5/$, in english, is that "the right to buy 1$ for 1.5AUD" or "the right to buy 1.5AUD for 1$"? Please help me :)
Either option could exist, so you should be clear whether the underlying is USD or AUD. I will base my answer only on what you have written.
Normally the strike price is expressed in terms of the price of the underlying. The currency in the denominator is the underlying (you get one unit of it) and the currency in the numerator is the numeraire (what you pay to get a unit of what's in the denominator).
The way you have expressed it, one USD has a cost of 1.5 AUD. I would say, then, that the underlying is a USD. You therefore have "the right to buy one USD for 1.5 AUD." If the spot price rises above the strike, that would mean it costs more than 1.5 AUD to purchase a single USD. In other words, dollars are becoming more expensive (stronger) and your call option is in the money.
For the opposite option, the strike price should be quoted in terms of USD. In other words, if AUD was the underlying, its price would be 0.67 $/AUD.
TL;DR answer: when a strike price is given, the thing after the slash is what you have the right to buy with a call option.