Multimedia Design is simply the use of a variety of artistic or communicative media. This includes text, graphic, audio, video etc.
Graphic Design is the foundation of every kind of design. It's the father of all. It includes Print Design, Graphic, Web everything. But to be exact graphic design is simple designing graphics. Say it designing a movie character, icons, cartoons, textures, backgrounds, logos, business cards, flyers, brochures and many more.
Web Design encompasses many different skills and disciplines in the production and maintenance of websites. The different areas of web design include web graphic design; interface design; authoring, including standardized code and proprietary software; user experience design; and search engine optimization.