The Western Hemisphere (west of Prime Meridian, east of Antimeridian) is bordered by three oceans:
Southern Ocean (or Antarctic waters) borders the southern extent (south of 60°S).
The question "ocean on the east side of Western Hemisphere" is slightly ambiguous. The Western Hemisphere's eastern boundary is the Prime Meridian (0°), which runs through Greenwich, UK. The Atlantic Ocean lies within the Western Hemisphere along its eastern coasts (Americas' east coasts). So the Atlantic is both in the Western Hemisphere and forms its eastern coastline.
No ocean lies entirely east of the Western Hemisphere—that would be the Eastern Hemisphere (Indian Ocean, parts of Atlantic).