Manga is the term for Japanese comics. The art work is very detailed and beautiful. Manga are often serialised in monthly publications such as Nakayoshi (Bishoujo Senshi Sailor Moon, Magic Knight Rayearth), Ribon (Marmalade Boy, Kodomo no Omocha) or Shonen Jump (Ruruoni Kenshin), and later compiled into graphic novels. In the United States, manga is usually available in the latter form, though you may be able to find the serialised publication in your local anime/comic shop or a Japanese grocery or book store.
A TV series is, well, an animated TV series. The series can be quite short, i.e. Neon Genesis Evangelion was 24 TV episodes, or long-running, i.e. Bishoujo Senshi Sailor Moon ran for 200 episodes. Compared to OAVs and movies, the animation quality in TV series is the poorest. However, that does not mean the animation is lacking in anyway, i.e. the animation in Ruruoni Kenshin is amazing!
Whether you prefer OAV or OVA, both terms refer to original animated video (OAV) or original video animation. OAVs are, as the term implies, animations directly released to video. The animation quality is better than a TV series, but not quite as good as a movie. An OAV can lead to a TV series (Kodomo no Omocha), continue a series (Wedding Peach Deluxe, Fushigi Yuugi), involve the characters from a series but completely change the plot (Magic Knight Rayearth), or be a complete story with no other animation history (Battle Angel Alita, My Dear Marie, Heroic Legend of Arslan). OAVs are stand alone (all background, characters are explained necessary for the story even in continuing OAVs) and usually short (between two to six episodes). I tend to think of OAVs as the equivalent to the US mini-series.
A movie is an animated theatrical release. Movies have a larger budget than a TV show or an OAV, and the animation quality reflects this difference. The animation is absolutely superb. Movies are stand along, but can either be a complete story with no previous animation history (X the Movie) or a side story with characters from a TV or OAV series (the Tenchi movies, Sailor Moon movies, Ruruoni Kenshin movie, End of Evangelion).
