'irregularly-employed' is a compound formed from 'irregularly' and 'employed'. 'irregularly' derives from 'irregular' + the adverbial suffix '-ly'; 'irregular' originates from Latin 'irregularis', where the prefix 'in-' (later 'ir-') meant 'not' and 'regularis' came from 'regula' meaning 'rule'. 'employed' is the past participle of 'employ', which comes from Old French 'employer' (to use or put to use), built from en- + a root related to Old French 'ployer' (from Latin 'plicare', 'to fold' or 'to ply').

'irregular' entered English via Latin and Old French influences and became Middle/Modern English 'irregular'; the adverbial '-ly' comes from Old English '-lic' and later formed 'irregularly'. 'employ' entered Middle English as 'employen' from Old French 'employer' and later simplified to modern English 'employ' with the past participle 'employed'. The compound 'irregularly-employed' is a modern English descriptive compound formed from these elements.

Originally 'irregular' simply meant 'not according to rule' and 'employ' primarily meant 'to use or put to use'. Over time 'employ' shifted toward the sense 'to hire someone for work', so the compound now specifically conveys being 'hired or working without regularity or permanence'.