My question is 3 fold;
1) Is it lawful for private collectors in Australia to own, buy or
sell antique Aboriginal remains - i.e. bones?
2) Is it legal for private collectors in the United states to own them?
3) Are museums in either country permitted to own/display item?
I think the display of human remains can often be disrespectful and
politically incorrect, but ethics aside, what are the legalities

Regarding the laws in the United States, this may be of interest to you:

http://www.ibsgwatch.imagedjinn.com/learn/lawsstate.htm