Senyuu 2 starts off right after the first season, continuing its almost non-exsistant plot. The direction is never clear and is made a bit more confusing by splitting the characters into different groups. It's not much of an upgrade over the first season and is frankly fairly boring.
Because its a very short gag show, everything is done for a laugh, so you can't except much out of the story-line. It keeps hinting at story advancement, but progress only happens every few episodes. However, it does move at a faster pace than the first season, which is an improvement. Now that all the characters are introduced, the story is allowed to actually go somewhere and not waste as much time on character intros.
Although diverse, none are particularly amazing. They're very simple because character development/originality is not important for this type of comedy. Rudolf's loli obsession makes him the most funny and memorable character, but the rest are fairly dull and forgettable.
It's important to note that I'm not a huge fan of quick gag comedy, which explains the low overall score. There are a few I've liked (Ishida to Asakusa for example), but most seem too 'dumb' to be actually funny. There are a few smiles in this (Rudolf's love for lolis is always amusing), but many of the jokes depend on being compeltely random, and not actually funny. When the joke is repeated a few times, I think the point of the joke (randomness) is gone and its not even remotely funny.
Overall, if you liked the first season, you'd probably enjoy the sequel. It is a slight improvement, although its serious flaws are still there. If you didn't enjoy the first season, don't bother sticking around! I did not enjoy either season and wanted to drop it after the first episode (I decided to add characters into the database for this show, so I stuck around). However, I did not like it because of the type of comedy. If you like quick gag comedy you might rate it much higher than me. My personal enjoyment was 3/10.