Is Waltzing Matilda comprehensible outside of Australia? In Australia?

I'm American, but it seems to me that when I’ve encountered Australian speech or writing, I didn’t have much trouble understanding it. The words are mostly familiar to me. So what’s going on in the song Waltzing Matilda?

An excerpt:

Once a jolly swagman camped by a billabong
Under the shade of a coolibah tree,
And he sang as he watched and waited till his billy boiled:
"Who'll come a-waltzing Matilda, with me?"

Chorus snippet

Down came a jumbuck to drink at that billabong.
Up jumped the swagman and grabbed him with glee.
And he sang as he shoved that jumbuck in his tucker bag:
"You'll come a-waltzing Matilda, with me."

I think that a typical American reader or listener will understand almost nothing of the story without discussion due to the strange vocabulary. For example, did the average British speaker know the Australian meanings of waltzing (an itinerant worker on foot) and Matilda (an affectionate term for a swag) back in 1895?

For that matter, do modern Australians understand this vocabulary easily and is the wording natural?

In addition, does the use of a lot of Australianisms reflect something about social class, the way Cockney English would?

My question is whether anyone ever naturally phrases his thoughts the way the singer does.

It was written in 1895, so much of the language which would have been current then would have developed. For example, Robert Burns' poetry is hard to understand now if you haven't had it explained (note it was written about 100 years before Waltzing Matilda). This will inhibit the average British speaker from understanding, but also Australia was (in part) colonised by British convicts, so the language will be that of the lower classes (class distinction was much more prevalent at this time) which makes it even harder to understand nowadays.

Also, since it has since become part of Australia's heritage (regarded as the 'unofficial National Anthem'), Australians are more likely to understand the lyrics since they would have been explained on their mother's knee, so to speak.

As to whether "anyone ever naturally phrases his thoughts the way the singer does," one must ask whether songs today accurately reflect the way people think currently.

I'm Australian and in my mid 50s. To answer your question as to whether modern Australians understand the vocabulary in Waltzing Matilda, anyone who was born or educated in Australia in my age group knows the meaning of quite a few of the words, and still uses some of the words particularly when out on camping trips. Some of the words are used in Australian television shows like Bush Tucker Man, or in modern camping and travelling shows. Others have been adopted as names of companies, brands, streets and shops. My children also understood all of the words below.

Jolly means happy - jolly fat Santa; someone with a big belly that shakes when he laughs; someone who laughs a lot. Still in use and understood.

Swagman - Someone who sleeps on a swag while camping out bush. Australian outdoor recreational stores like BCF still sell swags. A swag is a thin mattress with or without a personal tent attached to it.The swag can be rolled up tightly and carried on the back if you're hiking. My dad used to be a drover and he slept on a swag for years - his swag roll also had sheets, a pillow and a blanket - our family still use the blanket from his original swag. My son and daughter both own swags and use them on camping trips. In the Australian television series Bush Tucker Man - Les rolls out his swag when he's sleeping outdoors. Upmarket swags have mosquito nets or tarps. Swags for the homeless is an Australian welfare group that designs and distributes swags to homeless Australians. In Waltzing Matilda the swagman was itinerant and carrying his bed on his back rather than camping for fun or work purposes.

Billabong A waterhole or bush swimming hole. A wandering creek which may be dry part of the year. A clothing line in Australia specializing in outdoor/recreational clothes.

Coolibah tree. A common species of gum tree (Eucalyptus) found in Australia. Name of retirement village chain, street names etc.

Billy A can with a handle that you boil water in or can make tea in - still sold in camping stores in Australia. "Put the billy on" means "put the kettle on and make a cup of tea." Seen on some advertisements for tea packets and getaway outdoor advertisements.

Jumbuck - a sheep. More a rural term. Often used in advertising sheepskin or woollen products.

Glee - jumping up and down with excitement; grinning with pleasure. A bit old fashioned. People my age understand it though.

Tucker - food. Still in common use. Schools have tuck shops. Labourers wait for the tucker truck to come by. Tucker time means dinner time. Good Tucker means you like the food that's being served, the nutritional value of the food or how the meal tastes.