El-Hazard is the story of four people who were transported from Shinonome High School in the world we know, to the maginficent world, El-Hazard by the demon Ifurita.
Makoto Mizuhara - a Junior at Shinonome High, he is generally well-liked. He is smart, and athletic, and has a secret crush on Nanami Jinnai. When he is transported to El-Hazard, he is mistaken for the Princess Fatora of Roshtaria. He also gains the ability to communicate and control the ancient technology of El-Hazard.
Professor Masamichi Fujisawa - a teacher at Shinonome High, he drinks and smokes profusely. His favorite hobby is extreme mountain climbing. When he is transported to El-Hazard, he gains superhuman strength, speed, and agility. His powers are supressed when he is drunk, however, and his full powers are only active when he is sober and not smoking.
Katsuhiko Jinnai - a Senior at Shinonome High. After seeing that he placed second on an exam to Makoto, he decides that Makoto is his predestined rival, and must defeat him at all costs. When he is transported to El-Hazard, he quickly establishes himself as a great commander of the Bugrom, an insect-like race of beings who are trying to conquer El-Hazard.
Nanami Jinnai - Katsuhiko Jinnai's younger sister. She is a businesswoman by nature, and is always looking for a way to make extra money. When she is transported to El-hazard, she gains the ability to see through the illusions of the Phantom Tribe.
The story of El-Hazard begins as a seven-episode OAV, which takes place during the time of the Bugrom Invasion. During this time, Princess Fatora is kidnapped, Makoto & company arrive in El-Hazard, and the alliance that Roshtaria heads is clamoring for the Eye of God, an immensely powerful weapon, to be unsealed.
The OAV deals with the Bugrom Invasion, and how the four arrivals from Earth complicate things. Makoto is substituted for Fatora, and they go to visit the Muldoon Priestesses, the only people in El-Hazard with the power to unseal the Eye of God. At the same time, Katsuhiko Jinnai is rising within the ranks of the Bugrom, and attempting to kill Makoto. It is with Jinnai's help that the Bugrom are able to gain control of Ifurita, the last of the ancient Demon Gods. The series becomes a struggle between Jinnai, who is trying to conquer the world, and Makoto, who is only trying to do what's right.
El-Hazard is an excellent anime, in my opinion. The music is beautiful, the plotlines are excellently written, and the dialogue is superb. A must for any serious otaku.