Dgeigh, first of all I don't know which alleged etymology of 'Pom' you found - the most commonly accepted is an abbreviation of 'Prisoner of his/her Majesty'. (Australian humour dictates that Britain got it wrong in sending all the criminals off to the wide, sunny, blessed lands of Oz and leaving all the righteous citizens to endure their home winter, so who was a prisoner after all?)

As for rhyming slang, I find a continual minor irritation in all the tourist books along the lines of 'How to speak Strine' which list/translate perfectly good Cockney rhyming slang as if it originated in Australia. (Bit like 'as American as apple pie - just where did the Americans get apple pie from, I'd like to know?!? )

Bits of rhyming slang are still used. I'd quite happily say 'let's have a butcher's' and 'trouble and strife' is widely understood though not widely used.

Much more genuinely 'Australian' to my ear is the habit of abbreviating words to end in an 'o' - 'let's get the relos round for a barbie this arvo'. And there are some fantastic slang expressions:
- Act like a shepherd and get the flock out of here
- I must be off like a bucket of prawns in the sun
- flat out like a lizard drinking