Hi Alison
If you posted on the Immigrants to Australia board, more folks would probably see your post - and they could well have more information.
I've checked the online immigrant files I know about but cannot find your families. The NSW BDM records are online at
http://www.bdm.nsw.gov.au - follow the links through family history to search the indexes. I found a death for a William in 1922 - but not near Wollongong. The death index is only to 1945.
There are 3 marriages for your family name in Wollongong in the period to 1945 viz
19667/1928 SAMUEL EDWARD R OSMOND ALICE E V WOLLONGONG
16967/1933 SAMUEL IDRIS THOMPSON THELMA M WOLLONGONG
14525/1936 SAMUEL ALREMA EASTON EDITH WOLLONGONG
The only way to check the parents is to buy the certificates.
Thyer is such an unusual name, it would seem a good one to use for any searching.
good luck with the search
Trish