Old English ofer "beyond, above, upon, in, across, past; on high," from Proto-Germanic *uberi (cf. Old Saxon obar, Old Frisian over, Old Norse yfir, Old High German ubar, German über, Gothic ufar "over, above"), from PIE *uper (see super-). As an adjective from Old English uffera. As an adverb from late Old English. Sense of "finished" is attested from late 14c. Meaning "recovered from" is from 1929. In radio communication, used to indicate the speaker has finished speaking (1926). Adjective phrase over-the-counter is attested from 1875, originally of stocks and shares.
Old English eall "all, every, entire," from Proto-Germanic *alnaz (cf. Old Frisian, Old High German al, Old Norse allr, Gothic alls), with no certain connection outside Germanic.
Combinations with all meaning "wholly, without limit" were common in Old English (e.g. eall-halig "all-holy," eall-mihtig "all-mighty") and the method continued to form new compound words throughout the history of English. First record of all out "to one's full powers" is 1880. All-terrain vehicle first recorded 1968. All clear as a signal of "no danger" is recorded from 1902. All right, indicative of approval, is attested from 1953.