Some countries will not issue visas to visitors with criminal records. It is best to check with the foreign consulate of the country concerned.
The Migration Act 1958 (Cth) s 203 provides for the deportation of non-citizens who are convicted of certain serious offences. As well, a visa may be refused or cancelled on character grounds [s 501].
See also the following section on Citizenship about dual nationals and the Immigration and Citizenship chapter of the handbook. See in particular the section on Visa cancellations under section 501 (character grounds).