Green’s Dictionary of Slang

a sexually available (young) woman; a prostitute.

c.1698		B.E. Dict. Canting Crew n.p.: Strum [...] a handsom Wench or Strumpet.
1713		W. King York Spy 43: Scarce one appeared above the Degree of an Alderman’s Pimp, nor one Strum, that cou’d demand above Two pence Wet and Two pence Dry, for a Nights Occupation.
1725		N. Ward Amorous Bugbears 28: As if her wealthy Keeper had borrow’d his Wife’s Girdle, out of her Casket of Jewels, to adorn his Mistress for the Day, that the proud Curtesan might appear the less like a Strum.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. c.1698].
1765		Harris’s List of Covent Garden Ladies 55: Who wou’d imagine from so mean a thing, / So fair a face, so sweet a Strum cou’d spring?
1836		‘Bill Stroke’Em’ in Gentleman’s Private Songster in Spedding & Watt (eds) Bawdy Songbooks (2011) III 380: One night he met a pretty lass, / He wanted much a strum.
1888–94		‘Walter’ My Secret Life (1966) V 1035: He thinks from a large acquaintance with these useful strums, that their cousins and friends [...] get the virginities for nothing, and before the girls are fifteen years old.
1914		E. Wittmann ‘Clipped Words’ in DN IV:ii 121: strum, from strumpet.