Oregon's rhymes with:
gilligan's, balbriggans, bargains, bennigan's, cardigans, copenhagen's, corrigan's, diegans, dorgan's, dougens, douggins, dragon's, dragons, feagans, flanigan's, flashguns, gergen's, gilligan's, goggans, gorgons, hagans, hagens, hargens, higgens, hooligans, jergens, juergens, junghans, jurgens, kerrigan's, machineguns, megan's, michigan's, morgan's, morgans, mulligans, organs, plagens, rattigan's, reagan's, reagans, reagans', regan's, shenanigans, siegan's, slobogin's, slogans, snapdragons, toboggans, vegans, volkswagen's, volkswagens, wagons, wiggans
Oregon's sounds like:
oregonians, organic, organics, organize, organizes, organs, orgasms, origins, orogenic