Old English stranglice "firmly, stoutly, boldly, bravely;" see strong (adj.) + -ly (2).
Entries linking to strongly
strong adj.
Old English strang "physically powerful, powerful in effect; forceful, severe, firm, bold, brave; constant, resolute; arduous, violent," from Proto-Germanic *strangaz (source also of Old Norse strangr "strong," Dutch streng "strict, rigorous," Old High German strang "strong, bold, hard," German streng "strict, rigorous"), possibly from PIE *strenk- "tight, narrow." Originally compared strenger, strengest (compare old/elder/eldest).
Grammatical sense, of noun and verb inflections, is first attested 1841, translating German stark, used in a grammatical sense by Jakob Grimm (the terms strong and weak better fit German inflections). Strong suit (1865) is from card-playing. Strong man "man of great strength" (especially one who displays it professionally) is recorded from 1690s; meaning "dominating man in a political organization" is from 1859.
-ly 2
common adverbial suffix, forming from adjectives adverbs signifying "in a manner denoted by" the adjective, Middle English, from Old English -lice, from Proto-Germanic *-liko- (cognates: Old Frisian -like, Old Saxon -liko, Dutch -lijk, Old High German -licho, German -lich, Old Norse -liga, Gothic -leiko); see -ly (1). Cognate with lich, and identical with like (adj.).
Weekley notes as "curious" that Germanic uses a word essentially meaning "body" for the adverbial formation, while Romanic uses one meaning "mind" (as in French constamment from Latin constanti mente). The modern English form emerged in late Middle English, probably from influence of Old Norse -liga.
strong adv.
Old English strange "strongly, violently, severely, furiously" (alongside strongly), from the same source as strong (adj.). Going strong (1898) is from racing. To come on strong was originally come it strong (1812).