case (n.1) Look up case at Dictionary.com
early 13c., "what befalls one; state of affairs," from Old French cas "an event, happening, situation, quarrel, trial," from Latin casus "a chance, occasion, opportunity; accident, mishap," literally "a falling," from cas-, past participle stem of cadere "to fall, sink, settle down, decline, perish" (used widely: of the setting of heavenly bodies, the fall of Troy, suicides), from PIE root *kad- "to lay out, fall or make fall, yield, break up" (cognates: Sanskrit sad- "to fall down," Armenian chacnum "to fall, become low," perhaps also Middle Irish casar "hail, lightning"). The notion being "that which falls" as "that which happens" (compare befall).

Meaning "instance, example" is from c.1300. Meaning "actual state of affairs" is from c.1400. Given widespread extended and transferred senses in English in law (16c.), medicine (18c.), etc.; the grammatical sense (late 14c.) was in Latin. U.S. slang meaning "person" is from 1848. In case "in the event" is recorded from mid-14c. Case history is from 1879, originally medical; case study "study of a particular case" is from 1879, originally legal.
case (n.2) Look up case at Dictionary.com
"receptacle," early 14c., from Anglo-French and Old North French casse (Old French chasse "case, reliquary;" Modern French châsse), from Latin capsa "box, repository" (especially for books), from capere "to take, hold" (see capable).

Meaning "outer protective covering" is from late 14c. Also used from 1660s with a sense "frame" (as in staircase, casement). Artillery sense is from 1660s, from case-shot "small projectiles put in cases" (1620s). Its application in the printing trade (first recorded 1580s) to the two trays where compositors keep their types in separate compartments for easy access led to upper-case letter for a capital (1862) and lower-case for small letters.
"The cases, or receptacles, for the type, which are always in pairs, and termed the 'upper' and the 'lower,' are formed of two oblong wooden frames, divided into compartments or boxes of different dimensions, the upper case containing ninety-eight and the lower fifty-four. In the upper case are placed the capital, small capital, and accented letters, also figures, signs for reference to notes &c.; in the lower case the ordinary running letter, points for punctuation, spaces for separating the words, and quadrats for filling up the short lines." ["The Literary Gazette," Jan. 29, 1859]
case (v.) Look up case at Dictionary.com
"enclose in a case," 1570s, from case (n.2). Related: Cased; casing. Meaning "examine, inspect" (usually prior to robbing) is from 1915, American English slang, perhaps from the notion of giving a place a look on all sides (compare technical case (v.) "cover the outside of a building with a different material," 1707).