In the Akatsuki, Pain was the leader, but sometimes the other members would do things that were completely against his orders in a rather funny way. For instance, Zetsu would sometimes disappear without notice during important meetings, and when Pain asked about it, Zetsu would come back with some absurd excuse like he was following a special 'plant - mission'. It was a running joke among the members how Zetsu always had his own agenda.
There is a story where Tobi was trying to be all mysterious and cool, but he ended up getting his mask stuck in a tree branch while jumping around. His flailing to get it free was quite a sight. The other members just watched in amusement.
A really funny Akatsuki story is when Konan was trying to teach some of the new recruits basic combat skills. She was demonstrating a move, but one of the recruits misinterpreted it completely and ended up falling flat on his face. Konan couldn't help but laugh, which was quite rare for her. This incident lightened the usually serious mood in the Akatsuki's training area.
One interesting fanfiction is when the Akatsuki attempts to make a music video for recruitment purposes. Deidara is in charge of the special effects, which end up being more like explosions. Kisame is made to sing, but his deep voice makes it sound like he's growling rather than singing. Konan tries to choreograph the dance, but everyone has their own ideas and it turns into a chaotic mess. This shows the Akatsuki in a completely different and humorous light.
Deidara is also a great character in funny fanfictions. His explosive art can create chaos in a humorous way. Like when he tries to show off his art to the other members and accidentally blows up their hideout's roof. His passionate rants about art can also be really funny when contrasted with the more serious Akatsuki members.
Well, one interesting aspect could be the unique character interpretations. In an 'akatsuki funny fanfic', the writers might give the Akatsuki members really comical personalities that are different from their usual serious portrayals in the original work. For example, they could make Hidan be afraid of something really silly like a small insect, which is a big contrast to his tough - guy image.
One funny Akatsuki story could be about Deidara and his explosive art. Once, he was trying to show off a new type of explosive to Sasori, but it backfired and ended up blowing up his own hair. He looked like a porcupine for a while, which made Sasori laugh, a rare sight indeed.
One funny Akatsuki fanfiction story could be about Hidan and Kakuzu's constant bickering. Hidan, being his crazy self, decides to play a prank on Kakuzu by 'hiding' his money bags. When Kakuzu finds out, he chases Hidan all around their hideout, with Hidan laughing hysterically while Kakuzu is fuming. It's a humorous take on their odd relationship within the Akatsuki.
In a fanfiction, the Akatsuki members decided to have a talent show. Deidara thought his art was the best talent and started showing off his explosive sculptures. But then Tobi got up and did a really goofy dance that had everyone laughing, including Sasori who usually never shows any emotion. It was so unexpected that even Itachi cracked a small smile.
Well, there's the story of the Christmas play at a local church. One of the kids playing an angel got so nervous that instead of saying his lines, he started singing 'Jingle Bells' at the top of his lungs in the middle of the serious scene. Everyone in the audience burst out laughing. It was quite a memorable moment.
There was a fundraising concert where the lead singer of the local band forgot the lyrics of their most popular song. Instead of panicking, he started making up the silliest lyrics on the spot. The audience found it so funny that they donated even more money than expected for the cause. It was a great example of how an unexpected mishap can turn into a successful fundraising moment.
One interesting story was about a Soviet school. The teacher asked the students to write an essay about their future. One student wrote that he wanted to be a potato farmer. When the teacher asked why, he said that potatoes were very important in the Soviet diet, and he wanted to make sure everyone had enough. His simple and practical answer made the whole class laugh.
One funny story is about a pioneer who thought he could tame a wild horse by just talking to it gently. He stood there for hours chatting away to the horse, which just stared at him blankly. Eventually, the horse ran off, leaving him looking rather silly.