Its recommended to watch the anime first as the OVA takes place after key events of the series. Episodes 1 & 2 feel like extended Nube episodes, however Episode 3 has the feel of a movie.
As expected of OVA series, the animation is of higher quality which is more noticeable in the prologue & some scenes. The same goes for the OST being new & performed by Masamichi Amano whose done soundtracks for several OVAs, however the biggest highlight is the last episode which will be explained in more detail down below.
Episode 1: Students have been disappearing around campus which is the act of a
ghost that hides in the walls. Nube is nearly captured by the ghost as he extracts his soul in the form of a boy Together with his students, Nube must regain his body, save the children, & exorcise this phantom. Overall alright episode as it displays the affection the students have for their teacher Nube.
Episode 2: A young ghost girl enters the dreams of Nube's students in which they must listen to complicated instructions on a path to find her harmonica, however if one takes the wrong path, they'll forever rest in peace. The story behind this OVA is a very creepy one but manages to deliver a heartwarming ending as Nube discovers the grief behind this girl.
Episode 3: THIS IS THE BEST ONE!! A demon named Zekki has come from the 6th level of Hell in order to rescue his brother Baki from Nube's seal. Meanwhile Nube's seal is getting weaker as Hell itself will soon feast itself on Earth. The animation for this episode is very unique as it almost resembles a different studio even though it's still animated by Toei. The character designs have more of a "pop" to them as their hairstyles, color & detail seem more "movie exclusive". Interesting thing about this OVA is that it really resembles a Go Nagai series as the author & artist of Hell Teacher Nube were inspired by Devilman among other series. With its near perfect blend of comedy & horror, certainly gives this episode a Go Nagai vibe along with delivering as something you won't see in the anime. There isn't that much violence but certainly feels more like a dark battle shonen with the great animation of demon battles.
Overall, this OVA series is great with the final episode being the perfect way to end it.