Green’s Dictionary of Slang

strum v.

1. to have sexual intercourse; thus strumming n., sexual intercourse.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]Lex. Balatronicum.
[UK]Byron Beppo ii: Prudery flings aside her fetter [...] Giggling with all the gallants who beset her; And there are songs and quavers, roaring, humming, Guitars, and every sort of strumming.
[UK]Egan Grose’s Classical Dict. of the Vulgar Tongue.
[UK] ‘There’s Somebody Coming’ in Ri-tum Ti-tum Songster 37: O lor, deary me, how you are stuffing and strumming.
[UK] ‘The Chaffing Family’ in Nobby Songster 13: There’s Dick he chaffs Poll, about strumming all night.
[UK]‘Walter’ My Secret Life (1966) II 247: While the strumming was going on in the parlour, people bought cigars, and tobacco [...] little did they guess the fun going on behind that red curtain.

2. to masturbate.

[UK]‘The Amiable Family’ in Fal-Lal Songster in Spedding & Watt (eds) Bawdy Songbooks (2011) III 8: My daughter Selina Jane Anna, / Practizes upon the pianner, / She is such a rum ’un, / She is always a strumming, / Such a inweterat manner.
[UK]Cythera’s Hymnal There’s my daughter Paulina Jane Anna, / Plays very well on the piano, / But sahe’s such a rum ’un, / She’s always a strumming / In such an inveterate manner.

3. (US, also strum heads, strum someone’s head) to hit; to fight; thus head-strumming n., hitting someone.

[US]B. Jackson Thief’s Primer 72: When they was strumming my head, the sheriff there said, ‘Cut it out, you can’t do that here.’.
[US]C. Shafer ‘Catheads [...] and Cho-Cho Sticks’ in Abernethy Bounty of Texas (1990) 215: strum heads, v. – to fight.
[US]Jackson & Christian Death Row xvii: Head-strumming is hitting someone.

In derivatives

strummer (n.)

the penis.

[UK]‘Fleet Street Blowing’ in Out-and-Outer in Spedding & Watt (eds) Bawdy Songbooks (2011) IV 130: None now I need withold / However large the strummer / [...] / If fellows can but pay.

In phrases

strum oneself off (v.)

to masturbate.

[UK]K. Sampson Powder 467: Sorry, I just had to go and strum myself off.