Season 1 - Princess Valkyrie crashlands on Earth like any other alien, except she lands on Kazuto, a small time bath-house owner. To save him from death she gives him part of her soul. However loaning your soul does have its ups and downs. Having halved her soul Valkyrie has reverted into her child self. Kazuto and friends, with a spaceship crashed on his bath-house, must now deal with everyday challenges and trouble while trying to figure out how to get Valkyrie back to normal... including more crash landings.
Season 2 - Valkyrie, Kazuto, Akina, Hydra and friends are back for more when the Key of time suddenly appears along with many other mysterious happenings. All seemed to be linked to a person named 'Valkyrie Ghost' who's only goal is stealing Kazuto for herself. As they team up against this seeming unbeatable foe they dig deeper into the mysterious past of Valkyrie's home planet, Valhalla
Season 3 - The third season doesn't have a particular story behind everything (like "Valkyrie Ghost" in the second season). It just tells 6 stories about the life of Kazuto & Co. with some additions: Raine and Chorus get a house on earth, the last three Valhalla princesses each get an episode, and in the last episode Kazuto and Valkyrie, who in the same episode managed to stay adult, >try< to marry again
Season 4 - Now with two Valkyrie's, everyone at the bathhouse tries to continue on with their normal lives, even though there's always trouble.
Note: Episodes 13-31 are English dubbed. sorry for the inconvience.