Etymology
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walk (n.)

c. 1200, "a tossing, rolling;" mid-13c., "an act of walking, a going on foot;" late 14c., "a stroll," also "a path, a walkway;" from walk (v.). The meaning "broad path in a garden" is from 1530s. Meaning "particular manner of walking" is from 1650s. Meaning "manner of action, way of living" is from 1580s; hence walk of life (1733). Meaning "range or sphere of activity" is from 1759. Sports sense of "base on balls" is recorded from 1905; to win in a walk (1854) is from horse racing (see walk-over). As a type of sponsored group trek as a fund-raising event, by 1971 (walk-a-thon is from 1963).

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walk-over (n.)
"easy victory," 1838, such as one that happens in the absence of competitors, when the solitary starter, being obliged to complete the event, can traverse the course at a walk. Transferred sense of "anything accomplished with great ease" is attested from 1902. To walk (all) over (someone) "treat with contempt" is from 1851.
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walk (v.)

"travel on foot," c. 1200, a merger of two verbs, 1. Old English wealcan "to toss, roll, move round" (past tense weolc, past participle wealcen), and 2. wealcian "to roll up, curl," from Proto-Germanic *welk- (source also of Old Norse valka "to drag about," Danish valke "to full" (cloth), Middle Dutch walken "to knead, press, full" (cloth), Old High German walchan "to knead," German walken "to full"), perhaps ultimately from PIE root *wel- (3) "to turn, revolve."

The shift in sense is perhaps from a colloquial use of the Old English word or via the sense of "to full cloth" (by treading on it), though this sense does not appear until after the change in meaning. In 13c. it is used of snakes and the passage of time, and in 15c. of wheeled carts. "Rarely is there so specific a word as NE walk, clearly distinguished from both go and run" [Buck]. Meaning "to go away" is recorded from mid-15c. Transitive meaning "to exercise a dog (or horse)" is from late 15c.; meaning "to escort (someone) in a walk" is from 1620s. Meaning "move (a heavy object) by turning and shoving it in a manner suggesting walking" is by 1890. To walk it off, of an injury, etc., is from 1741. Related: Walked; walking.

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over- 

word-forming element meaning variously "above; highest; across; higher in power or authority; too much; above normal; outer; beyond in time, too long," from Old English ofer (from PIE root *uper "over"). Over and its Germanic relations were widely used as prefixes, and sometimes could be used with negative force. This is rare in Modern English, but compare Gothic ufarmunnon "to forget," ufar-swaran "to swear falsely;" Old English ofercræft "fraud."

In some of its uses, moreover, over is a movable element, which can be prefixed at will to almost any verb or adjective of suitable sense, as freely as an adjective can be placed before a substantive or an adverb before an adjective. [OED]

Among the old words not now existing are Old English oferlufu (Middle English oferlufe), literally "over-love," hence "excessive or immoderate love." Over- in Middle English also could carry a sense of "too little, below normal," as in over-lyght "of too little weight" (c. 1400), overlitel "too small" (mid-14c.), overshort, etc.

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over (prep., adv.)

Old English ofer "beyond; above, in place or position higher than; upon; in; across, past; more than; on high," from Proto-Germanic *uberi (source also of Old Saxon obar, Old Frisian over, Old Norse yfir, Old High German ubar, German über, Gothic ufar "over, above"), from PIE root *uper "over."

As an adjective from Old English uffera. The senses of "past, done,  finished; through the whole extent, from beginning to end" are attested from late 14c. The sense of "so as to cover the whole surface" is from c. 1400. Meaning "leaning forward and down" is from 1540s. The meaning "recovered from" is from 1929. In radio communication, it is used to indicate the speaker has finished speaking (1926).

Above expresses greater elevation, but not necessarily in or near a perpendicular direction; over expresses perpendicularity or something near it: thus, one cloud may be above another, without being over it. Over often implies motion or extension where above would not; hence the difference in sense of the flying of a bird over or above a house, the hanging of a branch over or above a wall. In such uses over seems to represent greater nearness. [Century Dictionary]

Phrase over and above (mid-15c.) is pleonastic, for emphasis. Adjective phrase over-the-counter is attested from 1875, originally of stocks and shares. To be (someone) all over "be exactly what one expects of (someone)" is by 1721.

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walk-through (n.)
also walkthrough, 1944, "an easy part" (in a theatrical production), from walk (v.) + through. Meaning "dry run, full rehearsal" is from 1959, from the notion of "walking (someone) through" something.
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walk-on (n.)
"minor non-speaking role," 1902, theatrical slang, from the verbal phrase walk on, attested in theater jargon by 1897 with a sense "appear in crowd scenes," from walk (v.) + on (adv.). Meaning "actor who has such a part" is attested from 1946. The sports team sense is recorded from 1974.
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fly-over (n.)
also flyover, 1901 of bridges, 1931, of aircraft flights, from fly (v.1) + over (adv.).
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sleep-over (n.)
1935, from verbal phrase; see sleep (v.) + over (adv.).
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walk-out (n.)
"strike," 1888, from walk (v.) + out (adv.). Phrase walk out "to leave" is attested by 1840. To walk out on a person "desert, forsake" is by 1913.
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