The "sea" in nausea is a coincidence. The word does contain a vessel, though: it is Greek for ship-sickness.
Greek naus means "ship," from an Indo-European root for "boat." From it came Ionic Greek nausia, in Attic nautia. Etymonline glosses it as seasickness, but also as nausea and disgust in general. Even in Greek, then, the sense was spreading beyond the deck.
Latin borrowed the word as nausea, and for the Romans it meant seasickness specifically. Latin also built a verb, nauseare, originally "to feel seasick, to vomit."
English took nausea directly from Latin in the early 15th century, with its first sense being vomiting. The Saturday Evening Post's word column suggests it probably entered through medicine, when Latin was the language of the educated. Etymonline notes that in English it "seems never to have been restricted to seasickness." Queasiness on land counted from the start, and air travel later added another setting.
The word's family has its own quarrels. Nauseate arrived in the 1630s. Nauseous, from around 1600, first meant inclined to nausea or easily made queasy. Etymonline calls that sense obsolete, and from the 1610s nauseous meant causing nausea. Etymonline records the advice that careful writers say nauseated for the feeling and keep nauseous for what is sickening to contemplate.
One possible relative is noisier than the rest. Some etymologists derive noise, through Old French, from Latin nausea in a sense like "disgust, annoyance." Others prefer Latin noxia, "injury," and the OED finds the sense of the word against both suggestions. The link is unproven.
The ship itself sails on in English. Nautical and nautilus come from the same Greek naus. So does the "-naut" in astronaut and cosmonaut, named as if space were another sea to sail.