Green’s Dictionary of Slang

1. a butcher.

1845		J. Lindridge Sixteen-String Jack 386: ‘Don’t give advice to others, greasy, you wouldn’t like to follow yourself,’ he said, quietly:— ‘Who do you call greasy?’ said the butcher, advancing, in a threatening attitude to Jack. ‘You,’ answered Jack.
1895		Crowe Aus. Sl. Dict. 33: Greasy, a butcher.
2003		McGill Reed Dict. of N.Z. Sl. 93: greasy A butcher, shearer, rural cook or fastfood cook. ANZ C20.
1941		Baker Popular Dict. Aus. Sl.

2. a cook, esp. in an institution.

1873		J.C.F. Johnson Christmas on Carringa 1: Bill [...] was our chef de cuisine [...] in the vernacular cook, or ‘greasy’ [AND].
1895		Coburg Leader (Vic.) 7 Sept. 4/1: The greasy says if that young man down East cuts him out of his Bertha he will commit suicide.
1918		Kia Ora Coo-ee 15 Sept. 14/3: Remember [...] those who strive to achieve the impossible, and have to submit continually to the indignity of such an epithet as ‘Greasy’ – remember our army cooks!
1924		(con. WWI) A.G. Pretty Gloss. of Sl. [...] in the A.I.F. 1921–1924 (rev. t/s) n.p.: greasy. A cook or butcher.
1931		Irwin Amer. Tramp and Und. Sl. 91: Greasy. — A cook, especially on a construction job or in a labour camp.
1949		Monteleone Criminal Sl. (rev. edn).
1953		T.A.G. Hungerford Riverslake 91: It’s a bad show for you to be working as a greasy.
2003		McGill Reed Dict. of N.Z. Sl. 93: greasy A butcher, shearer, rural cook or fastfood cook. ANZ C20.

3. (US) a garage mechanic.

1927

C. Coe Me – Gangster 220: Flop kept asking the mechanic: ‘You all set, now, Greasy?’.

4. fast or takeaway food.

2004

(con. 1960s-70s) T. Taylor Top Fellas 27/2: Greasies were thrown, but no punches.