Old English wadan "to go forward, proceed, move, stride, advance" (the modern sense perhaps represented in oferwaden "wade across"), from Proto-Germanic *wadanan (source also of Old Norse vaða, Danish vade, Old Frisian wada, Dutch waden, Old High German watan, German waten "to wade"), from PIE root *wadh- (2) "to go," found only in Germanic and Latin (source also of Latin vadere "to go," vadum "shoal, ford," vadare "to wade"). Italian guado, French gué "ford" are Germanic loan-words.
Specifically "walk into or through water" (or any substance which impedes the free motion of limbs) c. 1200. Originally a strong verb (past tense wod, past participle wad); weak since 16c. Figurative sense of "to go into" (action, battle, etc.) is recorded from late 14c. Related: Waded; wading.
Forbade to wade through slaughter to a throne,
And shut the gates of mercy on mankind,
[Gray, from "Elegy Written in a Country Churchyard"]
magical formula used in conjuring, 1630s, earlier Hocas Pocas, common name of a magician or juggler (1620s); a sham-Latin invocation used by jugglers, perhaps based on a perversion of the sacramental blessing from the Mass, Hoc est corpus meum "This is my body." The first to make this speculation on its origin apparently was English prelate John Tillotson (1630-1694).
I will speak of one man ... that went about in King James his time ... who called himself, the Kings Majesties most excellent Hocus Pocus, and so was called, because that at the playing of every Trick, he used to say, Hocus pocus, tontus tabantus, vade celeriter jubeo, a dark composure of words, to blinde the eyes of the beholders, to make his Trick pass the more currantly without discovery. [Thomas Ady, "A Candle in the Dark," 1655]
Compare hiccus doccius or hiccus doctius, "formula used by jugglers in performing their feats" (1670s), also a common name for a juggler, which OED says is "conjectured to be a corruption of" Latin hicce es doctus "here is the learned man," "if not merely a nonsense formula simulating Latin." Also compare holus-bolus (adv.) "all at a gulp, all at once," which Century Dictionary calls "A varied redupl. of whole, in sham-Latin form." As a noun meaning "juggler's tricks," hocus-pocus is recorded from 1640s.