Welcome my friends to a world of mystery, of magic and strange creatures... of a country in turmoil, only able to be rescued by a young woman from another world... welcome to the world of Fushigi -- er, El-Hazard! Although it may sound familiar in plot to a few other anime series (FY and Escaflowne spring to mind), don't get them confused! Yes, it's true that El-Hazard is also a world in which the coming of a girl from another planet is destined to save a country... but Mizuhara Makoto is scarcely your ordinary schoolgirl: primarily because Makoto is a guy! Unfortunately, that doesn't stop destiny... but I'm getting ahead of myself.
On the anime side, El-Hazard is an extremely popular world. It has spawned two Original Animated Video Series (OAVs -- think of them as TV mini-series) and two television series. Since we are setting out to watch the second OAV series, I will do my best to provide you with an idea of what happened in the first OAV series.
Our story follows young Mizuhara Makoto. He is an ordinary high school student when, fleeing one night from his adversary, Jinnai Katsuhiko (who has gone a bit... ahem... loopy, and blamed all his problems on Makoto), stumbles upon an ancient ruins underneath Shininome High School. There, he encounters a mysterious woman (?) who proceeds to use the last of her strength to transport Makoto to El-Hazard.
As it happens, not only is Makoto transported to El-Hazard, but so is everyone else who happens to be on the high school campus at the time. This includes Jinnai's younger sister, Nanami, Jinnai himself, and their alcoholic, chain-smoking teacher, Mr. Fujisawa. Makoto and Fujisawa end up in roughly the same place and manage to save a young woman from certain danger. It turns out that traveling across the dimensions has endowed Mr. Fujisawa with super powers (that, to his dismay, only work when he's sober). The young woman they save, Rune Venus, is a princess of the country Roshitaria. She flips when she sees Makoto; it turns out that he bears an incredible resemblance to Rune's kidnapped sister, Fatora.
El-Hazard, as Makoto and Mr. Fujisawa learn, is a world at war. The allied nations are fighting against the evil Bugrom. The allied nations fortunately hold an important card: the super-destructive weapon ("I shall call it a... 'Death Star'") named the Eye of God, that hangs in El-Hazard's sky. It is said that only the two princesses can operate the Eye of God, and so Rune manages to convince Makoto to impersonate Fatora in order to reassure the other nations that they still have control of the Eye of God. Rune has Makoto-as-Fatora set out to see the Priestesses of Mt. Muldoon to see if the Priestesses will let them unlock the Eye of God.
Jinnai and Nanami have also reached El-Hazard; Jinnai has allied himself with Queen Diva, leader of the Bugrom (his "superpower" is the ability to communicate with the Bugrom). He does fairly well, conquering several areas of El-Hazard, and gets even crazier than he was to begin with, swearing vengeance against Makoto (Note: no, I didn't leave out anything in their history... he really is that crazy). Nanami has managed to find a job as a waitress in order to make money, and she runs into Makoto and Fujisawa when they go to meet the Priestesses. Fujisawa "saves" the chief priestess, Miz, and she is immediately smitten with him (a fact with which he doesn't seem entirely comfortable). The Priestesses discover that Makoto is not Fatora, yet decide to help him out (mostly due to Miz's infatuation with Mr. Fujisawa). The other two priestesses are Shayla-Shayla, the Fire Priestess (who ends up competing with Nanami for Makoto's affections), and Afura Mann, the Air Priestess.
Nanami exercises her superpower, the ability to see through illusions, when a member of the Phantom Tribe tries to kill Makoto. The Phantom Tribe, as we later learn, is led by Gallus (who, up until they find out that he is a member of the Phantom Tribe, is engaged to Rune Venus). The Phantom Tribe seem to have their own agenda of destroying everyone else on El-Hazard, and to those ends, have kidnapped Princess Fatora to try and figure out what lets her activate the Eye of God.
Jinnai learns of another super-weapon, this one even more powerful than the Eye of God: an ancient demon named Ifurita. Whoever awakens the demon with her Key of Power becomes her master. Makoto and Jinnai race to find Ifurita, and Jinnai manages to awaken her first. Makoto recognizes her as the woman who sent him to El-Hazard. Jinnai uses Ifurita to easily incapacitate the three priestesses, but when he tries to have her take out Makoto, Makoto uses his superpower (the ability to interface with ancient devices from El-Hazard) to free her from the bind to the Key and become her own master.
This is, necessarily, a condensed version of the events that pass. There is, of course, more, including a purple-haired lesbian, a magical cat which acts as armor, and, of course, Jinnai's really, really insane laughter. While this hopefully provides enough insight to follow the second OAV series, I highly recommend viewing the first OAV series, as it is very widely available (just re-released on VHS) and an excellent piece of animation (plus, it's only roughly four and a half hours long). Anyway, sit back, relax and enjoy El-Hazard 2, The Magnificent World.