A swag is a bedroll, like a sleeping bag. This is what the swagman carries with his belongings therein.
A squatter was originally a man granted land by the government to settle in Australia. Land was given to ex-convicts and free settlers who came to farm. These people became the landed middle-classes, the squatocracy, the natural enemy of the worker and the economic backbone of the colonies.
Tucker is food, and is tucked in to. It is kept in a tucker bag.
A billabong is not a creek. It is that part of a geographically old river, such as those common in Australia, that has meandered so far it is now cut off from the rest of the river. In effect, it is a horseshoe shaped pond. In the rest of the world, it is called an 'oxbow lake'.
A billy is in fact a tin can with a looped wire handle to hook over a stick. The stick is used to hold the billy over a campfire. You can make tea or stew in it. When you make tea it is called billy-tea, and you eat the stew or tea with damper, which is a simple fire-cooked bread.
The word 'swagman' does not have the negative connotations that hobo does. The swaggies were a necessary part of the labour force of the day and squatters offered hospitality of the best kind they could to swagmen. A better equivalent would be perhaps a peddlar.