Can people on ships feel earthquakes?

Yes, but earthquakes out in sea come across in the effect of tidal waves. When there is a shift in the earth's surface (yes it happens under water as well) the imbalance causes great swells in the ocean, lake, etc and the force of the quake creates huge waves, also known as Tsunami waves.

Out at sea, as opposed to close to shore, the only effect is a slight rise and fall of the sea as huge (not high) swells radiate from the earthquake's epicenter. Often such swells go completely unnoticed.