"Australia" does not have laws about such things: each state, territory and the Federal government has its own laws. Therefore I will base this answer on the laws of New South Wales.
Trespass in General
From the State Library of NSW:
Under the law of trespass, if someone enters the property without permission you can ask them to leave. If they refuse to go when asked, they are trespassing and you can use reasonable force to remove them.
Rather than resorting to force to remove the trespasser, you can call the police immediately and ask them to come and remove the trespasser and charge them. Under the Inclosed Lands Protection Act 1901 (sections 4, 4A, 4AA and 4B), where the land is fenced or enclosed, there are various penalties for unlawful entry and offensive conduct. With or without a fence, you may also be able to sue the trespasser if damage or injury has been caused.
The penalty under the Inclosed Lands Protection Act 1901 is 5 penalty units and in 2017 a penalty unit is $110 (= $550).
If they had entered with the intent to commit a serious indictable offence (they haven't) then this would trigger the breaking and entering provisions of The Crimes Act 1900 which has substantially larger penalties.
Access as a Landlord
NSW Fair Trading summarizes the relevant law. Basically, they can enter if the tenant gives permission or if they have complied with the notice periods: these are different for different reasons for the access. The following reasons require no notice:
To carry out urgent repairs, such as fixing a burst water pipe, a gas leak or a blocked toilet
In an emergency
If you [the landlord] have tried to contact the tenant and been unable to do so and have reasonable cause for serious concern about the health or safety of the tenant or other occupants
If you [the landlord] reasonably believe the premises have been abandoned
In accordance with a NSW Civil and Administrative Tribunal order
If they enter without having the right to do so, you can
- apply to the Tribunal for orders:
- to stop the landlord/agent entering the premises (Apply within 3 months after you become aware of the landlord’s/agent’s breach.)
- to specify or limit the days and times on which, and purposes for which, the landlord/agent or other authorised person can enter (Apply at any time during the tenancy.)
- for the landlord to carry out a term of your residential tenancy agreement (Apply at any time during the tenancy.)
- to allow you to change the locks or refuse the landlord a key to the premises
- to end your tenancy
- for compensation for loss of or damage to your goods (Apply within 3 months after you become aware of the loss or damage.)
- report trespass to the police (see above)
- complain to NSW Fair Trading.