Wheel shows the wh- that Old English wrote as hw-: the original was hweol, and scribes later reversed the pair. The word is native and very old, from a Germanic form with relatives in Old Norse hvel and Middle Dutch weel.
What makes it worth a second look is its ancestor. The Indo-European form was a reduplication of a root meaning "to revolve, move round" — the root doubled up on itself, roughly "the turn-turn." The same reduplicated form, taken through Greek kyklos, gives English cycle, and through other routes gives chakra and, at a distance, colony. So wheel and cycle are the same ancient word, one inherited directly through Germanic and one borrowed from Greek two thousand years later, which is why they look nothing alike and mean nearly the same thing.
wheel (n.) Middle English whele , disk or circular frame attached to the axle of a vehicle to help it go, from Old English hweol , hweogol , from Proto-Germanic *hwewlaz (source also of Old Norse hvel , Old Swedish hiughl , Old Frisian hwel , Middle Dutch weel ), from PIE *kw(e)-kwl-o- "wheel, circle," suffixed, reduplicated form of root *kwel- (1) "revolve, move round; sojourn, dwell." The figurative sense is by early 14c. To go on wheels in figurative use, implying rapid and continuous action, is by 1540s. Also from c. 1200 as an instrument of torture, variously used. Of cheese made in a circular form by 1977. The phrase wheel of fortune is attested from early 15c. (the image of Fortune's wheel is in English from 12c.). Wheels is by 1959 in slang as "automobile." Earlier wheels was "machinery," hence "motive power, principle of life." Wheel as slang for "important person, big shot" is by 1933, American English. The U.S. wheel-bug is so called by 1815. wheel (v.) c. 1200, whelen , "turn like a wheel, turn on or as on an axis or about a center," c. 1200, from wheel (n.); the transitive sense of "cause to move in a circle, cause to turn as on an axis" is attested from late 14c. As "turn and face a different direction," by 1630s. Related: Wheeled ; wheeling . also from c. 1200