buying his books could be difficult - I can't see any on book sites.

You will probably find the words of some/many of his poems on poetry sites.

check out the National Library's catalogue

Oral History interview - Alan Scott folklore collection, recorded 1955. Conversation and recitation.
Ted Harrington, Australian bush balladeer, speaks of his work and recites some of his poems [sound recording] / Interviewer: Stephen and Nita Murray Smith

Songs of war and peace by Edward Harrington. Melbourne : Fraser & Jenkinson, 1920.

Boundary bend and other ballads by Edward Harrington. Melbourne : Lothian, [1936?]

The Kerrigan boys and other Australian verses by Edward Harrington. Melbourne : W. Andrade, 1944

Alice Springs by Edward Harrington ; with portrait by Harry Hastings Pearce. Footscray, Vic. : Harry Hastings Pearce, 1957. Limited edition of 100 copies numbered and signed both by the author and illustrator.

The swagless swaggie and other ballads : selected verse of Edward Harrington. Melbourne : Australasian Book Society, 1957.