I read through all of the online digital records in the National Archives of Australia for Julianna's son's family.
It appears they were WWII refugees departed from Bremen, Germany who came to South Australia in 1950 to work on the railroad and were originally housed in Camp Woodside.
https://en.wikipedia.org/wiki/Woodside_Barracks
As eastern Europeans that survived Nazi Germany and didn't end up behind the iron curtain, they have a compelling WWII story.
I don't know the family members well enough to know if other refugees to Australia named SMOLKA were relatives but I suspect they were not. So my guess is there are not any cousin records that might contain clues.
Aniela, according to the archives was Roman Catholic. So my suggestion is to begin searching through parish records for Juliana Ligoń in and around Katowice (start with whichever parishes control records for Dąbrowa Górnicza, Będzin, Katowice, Poland). Parish birth records for Eugeniusz in 1923 can yield important info. Also check for years before and after for siblings (watch house numbers if you have them). I am not familiar with Silesian records. Maybe Skye or Maggie can point you to a resource. If you do find helpful resources to navigate these parish records, contribute your knowledge to the Silesian space page.
At the time of the partition the population of this village was 184. With the discovery and exploitation of coal, the population exploded to 40,000 at the time of Eugeniusz' birth. This growth wasn't organic, people moved into the area for economic opportunity. So the parish record hunt may not be easy. Górnicza translates to "Mining".
I think you should also get the Australian naturalization records for Eugeniusz and Aniela in 1957. Their 1956 application digital image isn't on the NAA site, but they have a process to request a copy if you haven't already done so.