Unhinged rhymes with:
hinged, binged, cringed, hinged, impinged, infringed, singed, arranged, avenged, binged, changed, cringed, deranged, estranged, exchanged, expunged, hinged, impinged, infringed, lunged, plunged, prearranged, ranged, rearranged, scrounged, shortchanged, singed, sponged, unchallenged, unchanged
Unhinged sounds like:
umscheid, umstead, unangst, unannounced, unassisted, unchecked, uncoat, uncoated, uncouth, unctad, uncut, unionist, unionized, unissued, unjust, unmanaged, unmasked, unmixed, unquote, unsaid, unscathed, unseat, unseated, unset, unstated, unsteady, unsuited, unswayed, unused, unwashed