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.