Old English æfter "behind; later in time" (adv.); "behind in place; later than in time; in pursuit, following with intent to overtake" (prep.), from of "off" (see off (adv.)) + -ter, a comparative suffix; thus the original meaning was "more away, farther off." Compare Old Norse eptir "after," Old Frisian efter, Dutch achter, Old High German aftar, Gothic aftra "behind;" also see aft. Cognate with Greek apotero "farther off," Old Persian apataram "further."

From c. 1300 as "in imitation of." As a conjunction, "subsequent to the time that," from late Old English. After hours "hours after regular working hours" is from 1814. Afterwit "wisdom that comes too late" is attested from c. 1500 but seems to have fallen from use. After you as an expression in yielding precedence is recorded by 1650.

Middle English fer, from Old English feorr "far, remote, distant," from Proto-Germanic *ferera- (cognates: Old Saxon fer, Old Frisian fer, Old Norse fjarre, Dutch ver, Old High German ferro, German fern), probably a development in western Proto-Germanic from the adverb (see far (adv.)). Far East "China, Japan, and surrounding regions" is from 1838.

Old English forð "forward, onward, farther; continually;" as a preposition, "during," perfective of fore, from Proto-Germanic *furtha- "forward" (source also of Old Frisian, Old Saxon forth "forward, onward," Old Norse forð, Dutch voort, German fort), from extended form of PIE root *per- (1) "forward." The construction in and so forth was in Old English.

c. 1400, from Old English inra, comparative of inne (adv.) "inside" (see in (adv.)). Similar formation in Old High German innaro, German inner. The original order of comparison was in/inner/inmost; the evolution has been unusual for a comparative, and inner has not been used with than since Middle English.

Inner man "the soul" is from late Old English; as "the spiritual part of man" by late 14c. The Quaker inner light is attested by that name from 1833. Inner tube in the pneumatic tire sense is from 1894. Inner city is attested from 1690s; as a euphemism for "urban poverty and crime," from 1963.

Old English oþer "second, the second of two; additional, further" (adj.), also as a pronoun, "one of the two; a different person or thing from the one in view," from Proto-Germanic *anthera- (source also of Old Saxon athar, Old Frisian other, Old Norse annarr, Middle Dutch and Dutch ander, Old High German andar, German ander, Gothic anþar "second, other").

These are from PIE *an-tero- (source of Lithuanian antras, Old Prussian anters "other, second), which is perhaps a variant of *al-tero- "the other of two" (source of Latin alter), from root *al- "beyond" + adjectival comparative suffix *-tero-.  Or the first element might be the pronoun *eno-, *ono- [Boutkan]. The Old English, Old Saxon, and Old Frisian forms show "a normal loss of n before fricatives" [Barnhart].

The sense of "second" was detached from this word in English (which now uses second (adj.), which is from Latin) and German (zweiter, from zwei "two") to avoid ambiguity. In Scandinavian, however, the second floor is still the "other" floor (Swedish andra, Danish anden). Also compare Old English oþergeara "next year."

As an adverb, "secondly" (late Old English); "otherwise" (c. 1200); "in addition" (mid-14c.).

The other woman "a woman with whom a man begins a love affair while he is already committed" is from 1855. The other day originally (late Old English) was "the next day;" later (c. 1300) "yesterday;" and now, loosely, "a day or two ago" (early 15c.). OED notes that the other place was euphemistic for Hell or "Oxford as regarded in Cambridge (and vice versa)." Phrase other half in reference to either the poor or the rich, is recorded from c. 1600.

La moitié du monde ne sçayt comment l'aultre vit. [Rabelais, "Pantagruel," 1532]

Halfe the world knowes not how the other halfe li[v]es. [George Herbert, "Outlandish Proverbs," 1640]

"that is farther out, that is exterior or external; of or pertaining to the outside; further removed," late 14c., comparative of out (on analogy of inner), replacing by 18c. forms descended from Old English uttera (comparative of Old English ut "out") which developed into utter (adj.) and was no longer felt as connected with out. Outer space "region beyond the earth's atmosphere" is attested from 1845.

15c. alteration of Middle English ferther (c. 1300), a variant of further (adv.). There is no historical basis for the notion that farther is of physical distance and further of degree or quality.

mid-15c., "assistance, support," also "advantage, benefit; advancement, promotion," from further (v.) + -ance.

c. 1200, from further (adv.) + more. There also was a farthermore in Middle English. Related: Furthermost.

late 14c., formed as superlatives to further (adj. and adv.).