One of his older brothers, William Hallett Stockdale (1887-1915), was killed in action at Gallipoli on 8 May 1915.
He married Ivy Gladys Lobb (1894-1947) in 1936.
He played with the Kilmore Football Club in 1917 and 1918.
Stockdale moved to Corowa to work (at Stockdale & Skehan Motor Garage ) and played football with his older brother, Chas Stockdale in the powerful Ovens and Murray Football League from 1920 to 1922. It was at Corowa Football Club that his football really started to excel. He was a member of Corowa's 1921 O&MFA grand final side that lost to . Stockdale managed to play seven games with Essendon Football Club between 1920 and 1922, before moving down to Melbourne permanently after the 1922 O&MFA season to play with Essendon.
A left footer, Stockdale started his career at Essendon as a half back flanker in 1920. After playing a full season for Corowa in 1922, Stockdale played his first match for the season with Essendon in round 15, then played as a forward in the 1922 preliminary final, against Fitzroy on 7 October 1922. Playing at full-forward he kicked five of Essendon's six goals (Essendon lost the match 6.9 (45) to Fitzroy's 9.14 (68)) — one of them (in the third quarter) with his right foot. He remained a forward for most of his career.
In the first match of the 1923 season, against St Kilda, Stockdale kicked 10 goals. In the 1923 season he kicked 68 goals and was the VFL league's leading goalkicker, breaking the record for the most goals kicked by a player in a season. He was the Essendon’s leading goalkicker in 1923 (68 goals), 1926 (36 goals), and 1928 (39 goals).
He won Essendon's Best and Fairest award in 1925; he was the team's vice-captain in 1928, and served as captain for one match in 1928. He represented Victoria in interstate football on 8 occasions (1923, 1925, 1927, and 1928).
Stockdale was reported for striking South Melbourne's Bill Berryman in the third quarter of the 5 May 1928 match at Windy Hill. Having heard evidence that Stockdale had struck Berryman four times in the back the VFL Tribunal suspended Stockdale for eight matches.
- "Stockdale, Greg". essendonfc.com.au. Archived from the original on 25 March 2012. Retrieved 6 April 2012.
- Deaths: Stockdale, The Argus, (Monday, 20 June 1927), p.1.
- Funeral Notices" Stockdale, The Argus, (Tuesday, 14 July 1925), p.1.
- Private William Hallett Stockdale, Australian War Memorial.
- Deaths: Stockdale, The Age, (Thursday, 10 July 1947), p.11.
- "Stockdale & Skehan Motor Garage, Corowa". Trove Newspapers. The Corowa Free Press.
- "1921 - O&MFA Grand Final match review". Trove Newspapers. The Corowa Free Press.
- Maplestone (1996), p.561.
- Football: Dash and Tenacity: Fitzroy Outlasts Essendon, The Argus, (Monday, 9 October 1922), p.4.
- Sharland,'Jumbo', "Gregory Stockdale the Big Gun of the Opening Day's Football", The Sporting Globe, (Wednesday, 9 May 1923), p.1.
- "The Argus 22 Oct 1923". Retrieved 6 April 2012.
- Maplestone (1996), p.373.
- Maplestone (1996), p.369.
- Maplestone (1996), p.379.
- Players Reported, The Sporting Globe, (Saturday, 5 May 1928), p.5.
- The League Tribunal: G. Stockdale (Essendon) Disqualified: Out for Eight weeks, The Age, (Friday, 11 May 1928), p.6; Football: League Tribunal: Charge Against Stockdale Upheld, The Argus, (Friday, 11 May 1928), p.6.
- League Stars for Association: Stockdale Joins Northcote, The Herald, (Monday, 14 January 1929), p.4.
- Football: Association Grand Final: The Teams, The Age, (Friday, 11 October 1929), p.7.
- Stockdale and Jenkins to be Association Coaches, The Herald, (Friday, 20 February 1931), p.7.
- Clearance of G. Stockdale, The Age, (Friday, 12 February 1932), p.5.
- Deaths: Stockdale, The Argus, (Monday, 16 May 1949), p.11.
- Mr. Greg Stockdale, The Narandera Argus, (Tuesday, 17 May 1949), p.2.
- Maplestone, M. (1996). Flying Higher: History of the Essendon Football Club 1872–1996. Essendon: Essendon Football Club. ISBN 0-9591740-2-8.