OK, an Aussie here!
Immigrants to Australia after WW2 seemed to have come in waves. At first we got the Europeans - Italians, Greeks, and Slavs, mostly. The Slavs don't seem to have given us much in the way of foods - certainly not as much as the Italians or Greeks. For those, the best known foods, still very popular, are things like Spaghetti Bolognese or Lasagne; the Greeks gave us Moussaka, Baklava, and salads with feta cheese.
Other Europeans, fewer in number, gave us Wiener Schnitzel and a variety of sausages, particularly salami. A lot of Germans settled in South Australia, and they've provided us with excellent wines.
Since Vietnam, there has been a huge influx of Vietnamese immigrants. These have introduced us to a huge range of Asian vegetables and sauces - most of which are called 'Thai' nowadays. Any stirfry using these vegetables (bok choy, Chinese cabbage, tatsoi etc) would be good examples of what have become popular.
The Chinese have been around since the goldrushes of the early 1800s. Their influence on our food has been immense, and continues. From them, we learned about things like straw mushrooms, bamboo shoots, water chestnuts and the like. Chicken and Almonds, or Mongolian Beef would be popular examples of their cuisine.
We get a lot of Indonesian foods here, too. Satays and Rendangs would be good examples of what is popular.
Indians and Pakistanis have made up a lot of our immigrant population. So curries would have to be included for that group.
In the 80s there was an influx of immigrants from the Middle East, especially Turkey and Lebanon. So we've learned about flatbreads and Kofta from them.
We've always had a great number of British immigrants, and they're still coming. This includes not only English, but Scots and Irish as well. We get fewer Welshmen, but think Potato and Leek Soup. Think Irish Stew or Colcannon (bubble and squeak); oatcakes from the Scots; steak and kidney pudding; bangers and mash; Toad in the Hole; Roast Beef and Yorkshire Pudding; fish 'n' chips from the Poms!
Although we haven't had a lot of immigrants from Central America, we've been quite strongly influenced by Mexican cuisine. Tacos, Chilli con Carne, and Burritos would be top of the list in that category.
We've had quite a few Japanese immigrants, but mainly they are our tourist trade, and we've had to learn to cater for them. So we've learned about Sushi and Teriyaki from them.
You can hunt up food from a large number of different countries at this site. It's fairly representive of what we get here in Australia.
Here are some sites that might interest you: