The first manga: (1992)
The series, originally known as Bannou Bunka Nekomusume, originally appeared 1992 in a 1-volume manga drawn by Takada Yuzo (3x3 Eyes), which also contained a story by Moriyama Yuji (character design and OVA director). As Takada was asked to work on the OVA, he only drew three chapters. In the book Nuku-Nuku is an android with a cat brain, extremely strong and intelligent, but with clear signs of her cat nature, always struggling to be more human. There were no fights, and the Mishima-Industries subplot is missing as well.
The first OVA: (1992-94)
For a summary see the excellent wu by PopeFelix. The OVA had 6 parts in total, and made the title character into a well-known commodity in Japan as well as the west. The role of Nuku-Nuku also helped cement the superstar status of seiyuu Megumi Hayashibara.
The second manga: (1997-98)
Mainly to promote the coming TV series, Takada was asked to draw another manga, Shin Bannou Bunka Nekomusume or New Cultural Catgirl, more oriented along the lines of the OVA than the first manga, and targeted at a younger audience. The 8 chapters tell the story of Nuku-Nuku's creation anew, with modern and fresh artwork, but somewhat flat characterizations and plots. It seems as if the manga was not produced on the initiative of the author but as a favor to the producers of the series.
The TV series: (1998)
Like the second manga, the TV series was directed at a younger audience, disappointing many older fans with a bland plot, flat characters and unfunny jokes. Nuku-Nuku is not so much a cat trying to fit in with human society, but rather a slightly daft girl with superpowers. Add to that a visibly low production budget causing sub-standard animation, and you are happy that there were only 12 episodes produced. The end-title pictures and songs (sung by Hayashibara) are very nice, however, and somewhat redeem the series.
The second OVA: (1998-99)
Known as Bannou Bunka Nekomusume Dash!, this 12-episode OVA changes the characters again. Ryunosuke is now 14, and thus at an age to be interested in Nuku-Nuku differently. The series becomes more of a love-comedy than an action-comedy. The series showed great potential and some episodes were very well written, but this series also had large visible budget troubles, with loads of cell-and-scene-recycling, and loads of pan-pictures instead of animated scenes, this OVA looks worse than many TV-series with respect to animation. The humor also falls short most of the time, no wonder as it was produced by the same team that was responsible for the TV-series.