To put it simply, the graphics of Overdose look like a full-rendered 3D anime. It took me a while to put my finger on the style. As you move through the huge levels, you will encounter cemeteries, office buildings and casinos that seem to come straight out of just about any modern anime. This isn't the cartoony style of the older animes; Overdose takes on the "not quite realistic" look found in shows like Ghost in the Shell, Trigun and of course, the GunGrave series.
The between-level cut scenes come in two flavors. For the major transitions in the game, you will be blessed with lengthy anime movies. The rest of the time, the story will progress via a conversation between the various characters, well stills of these characters that shake and jump around as they talk to each other. This last aspect caught me a little off guard at first, but at times served as a nice comedic relief.
As far as the music and sound effects are concerned, there isn't much to talk about. In general, the music was good and kept in the background most of the time, and the gunshots and bullet hits sounded about right. Basically, these features didn't hurt the game, but they didn't do a lot to pull me in either.