Nauseous comes from the Latin nauseosus, from nausea, seasickness. That goes back to the Greek naus, a ship, so the word first pointed to the sickness you feel at sea.
In British English each vowel letter keeps a sound: NAW-zee-us. In American English the s and the weak ee join into sh, the same kind of change that gives sh in special and nation. That makes two syllables: NAW-shus.
Usage guides once said nauseous should only describe things that cause sickness, like a nauseous smell, and that a sick person is nauseated. Today Cambridge and Oxford both give feeling sick as the first meaning.