There are only a small number of Sterrys found in church parish records.

New South Wales

Balmain West St Thomas, Anglican
Baptisms
+1914 Jun 10 [born 10 Nov 1913] William Alexander [Parents] John Andrew and Isabel D Sterrey [Abode] Melrose Short St [Profession of Father] Carter [Source: Anglican Parish Registers, Sydney, 1814-2011: Ancestry.com]
+1915 Nov 24 [born 22 Oct] Norman J [Parents] John A and Isabel Sterrey [Abode] 1 Short St [Profession of Father] Carter [Source: Anglican Parish Registers, Sydney, 1814-2011: Ancestry.com]
Marriage
+1913 Mar 26 John Andrew Sterrey, Bachelor, 24, Carter [Residence] Balmain [Born] Balmain [Father] Eli Sterry, Salesman [Mother] Katherine Bland & Isabell Doris McDougall, Spinster, 24, Home Duties [Residence] Balmain [Born] Balmain [Father] William Alexander McDougall, Ironworker [Mother] Sarah Ann Warland. Both signed. Wit: Henry George Rigg, June McDougall [Minister] Luke Parr [Source: Anglican Parish Registers, Sydney, 1814-2011: Ancestry.com]

Liverpool St Luke, Anglican
Burial
*1897 May 4 [died May 3] Henry Sterry, 38 years [Abode] asylum [Source: Anglican Parish Registers, Sydney, 1814-2011: Ancestry.com]

Sydney St Pauls, Cleveland Street, Anglican
Marriage
^^1946 Jan 9 Albert Edward Sterry, 21, Bachelor, Motor Driver R. N., [Born] Woolaston Gloucestershire England [Usual Place of Residence] 2 Primrose Hill, Lydney, Gloucestershire, England [Father] Oscar Sterry, Labourer [Mother] Anne Carroline(sic) Marshall & Iris Kathleen O'Connell, 20, Spinster, Machinist [Born] Sydney [Usual Place of Residence] 170 Botany Street Waterloo [Father] Daniel Patrick O'Connell, Labourer, deceased [Mother] Florence Jane Hargraves. Both signed. Wit: H G Turner, Dan O'Connell [Minister] F H Hordern. With consents of Thomas Aubrey Doolan, Stipendiary Magistrate.
[Source: Anglican Parish Registers, Sydney, 1814-2011: Ancestry.com]

Legend:

* = Bury St Edmunds Branch
+ = Longhope Sterry Branch
^^ = Minsterworth Sterry Branch
* = Lowestoft, Suffolk Branch