Okay, it turns out that all of this is covered under "Littering" in Part 5.6A of the "NSW Protection of the Environment Operations Act 1997". The relevant sections in this instance would be 144A, 145, 146A and 146B.
In short,
s144A - Definitions
advertising material means any paper product (including a leaflet, brochure or magazine), or other material thing, that contains advertising or promotional matter.
s145 - Littering generally
A person who deposits litter in or on a public place or an open private place is guilty of an offence.
Maximum penalty: 20 penalty units. ($2,200)
s146A - Depositing of advertising material
A person must not deposit any advertising material in or on any place, other than:
(a) in a receptacle that is provided for the deposit of mail, or
(b) in a receptacle that is provided for the deposit of newspapers, or
(c) under the door of any premises.
Maximum penalty: 5 penalty units. ($550)
s146B - Advertising material not to be placed in or on vehicles
A person must not deposit any advertising material in or on any vehicle.
Maximum penalty: 5 penalty units. ($550)
There are exceptions, so you should read the above sections in full.
(It's mostly plain English and easy to understand - unlike a lot of other legislation.)
To summarize, you pretty much need to obtain permission to do anything discussed in this thread except for the letter box drop.
The full Act can be found here:
www.legislation.nsw.gov.au/#/view/act/1997/156/whole
(There is also a "Party Pooper" clause at Section 146E that's worth reading if you have kids and an over zealous Council - I had no idea that one existed.)