The oil ship is a naval ship deployed on water like any other boat.
Oil boats are used to create oil rigs. To create any oil rig, blick Control units, direct your oil boat on to an oil spill (black cloud). Then, click Interface and click the blueish-black "Build oil rig" button.
Due to its relatively high health and extremely cheap cost, it can be used as cannon fodder for gunboats and battleships, assuming the unit cap isn't a problem.
The oil ship is the only naval unit that can increase income of the player. It is also the only naval unit that can change from a unit to a building.
It used to be a unit only accessible by right clicking the Docks, then clicking the button that said Oil Ship. It was still accessible by 1.3, although it used to be right-click 'exclusive' only.