It sounds like when you say “weird” you mean absurdist, so I’ll not recommend things like “Ping Pong the Animation” even though it’s both excellent and weird.

With that said, the absurdist anime I’ve seen in roughly descending order of preference are:

• Dan Da Dan - Takes itself a little more seriously than the examples you gave, but things still get very wild.
• BOCCHI THE ROCK! - Nothing absurdist about the plot, but the animators get very creative.
• Nichijou - My Ordinary Life - Most people already know what this is, so I’ll just say that City from the same author will be releasing later this year. I haven’t read it, but odds are it’s great.
• Akiba Maid War - Maid-themed Yakuza drama.
• Space Dandy - Cowboy Bebop if all the main characters were incompetent
• Cromartie High School - High school for delinquents.
• Zom 100: Bucket List of the Dead - Guy has an opportunity to finally leave his abusive company when zombies attack. He resolves to live each day as fully as possible and makes a list of things he wants to do before being turned into a zombie.
• Ghost Stores (the dub of course) - They realized this anime had no appeal as-is to a western audience so they made a batshit insane dub that only loosely follows the original story.

Some that haven’t been mentioned yet (I think):

• Kuuchuu Buranko: This one uses rotoscope animation. It’s a “trippy” anime that deals with various mental health problems (mostly OCD). I think this is one of those anime that almost nobody really knows about. It’s very obscure.

• Aku no Hana: This also uses rotoscope animation. I actually never watched the anime and only read the manga. It’s one of those psychological types but it’s well-grounded in reality. The animation itself is weird however. Probably because rotoscoping at this level is uncommon in anime.

• Monogatari Series: The notoriously “immoral” anime series (and one of my all-time favorites). Generally speaking, anything by SHAFT have really unique visual storytelling which includes Madoka Magica and Sangatsu no Lion.

If you can get past the part where it is pure, unabashedly crass, Panty + Stocking & Garterbelt oozes style. Actually, it oozes multiple styles, as it’s more than willing to switch from a ‘chibi’ style, to an overly ‘high-res’ style, and even to real world paper mâché within a single episode. It’s like nothing I’ve ever seen before, and certainly “built different.”

It’s also getting a second season after a decade, so there’ll be more of it soon.

Not sure on the exact flavor of “weird af” that Nokotan or Gintama get into since I haven’t seen them, but here’s some of the weirder shows I’ve watched:

• Nichijou
• Azumanga Daioh
• Penguindrum
• Utena
• FLCL
• Space Dandy

Thinking along a different style of weirdness, there’s also shows like Serial Experiments Lain – but I’m not sure if that’s what you’re looking for.

One anime that really is built differently, in structure, art style and themes:

Tatami Galaxy

Every episode is the main character making a different choice to try and fulfill his dream. It’s like Groundhog Day, but where Mr Groundhog eventually manages a perfect day, Mr Tatami learns to accept the imperfection of life.

Scene from Tatami Galaxy ep 9

Akiba Maid War had me laughing and saying “what the fucking is going on?” out loud a lot.

I like watching anime that’s build different:

Sonny Boy - Execution: S tier Weirdness: S tier

Kyousougiga - Execution: S tier Weirdness: S tier

Id: Invaded - Execution: A tier Weirdness: B tier

Flip Flappers - Execution: A tier Weirdness: B tier

Junk Head - Execution: A tier Weirdness: SS tier

Olympia Kyklos - Execution: C tier Weirdness: A tier

Train to the End of the World - Execution: B tier Weirdness: A tier

Dorohedoro is fantastically weird but solid world building and funny as fuck too.

Sokushi Cheat…, aka My Instant Death Ability is So Overpowered… sounds like a lousy isekai, but was surprisingly meta and funny.

Dead Dead Demons Dededede Destruction was really hard to watch, but it’s really good. It’s difficult to explain the appeal.

Shuumatsu Train Doko e Iku/Where Does the Doomsday Train Go? - Also a little difficult to watch, but really fun world building.

Elusive Samurai/Nige Jouzu No Wakagimi - A fun show that has style and is focused on meta instead of developing characters.

Samurai Flamenco - Both a tribute and parody of tokusatsu shows, that is entertainingly weird.

Hands Off Eizouken!/Eizouken Ni Wa Te Wo Dasu na - A beautiful tribute to the spirit of animators, but meta and funny at the same time. Better than this season’s Zenshuu.

Dead Leaves

So, OP wants weird anime. “Anime” anime.

• Odd Taxi
• Ping Pong Club
• Excel Saga
• FLCL
• Gantz
• Otaku No Video
• Way of the Househusband
• Golden Boy
• Colorful (of note, the English dub is heavily adapted to the point where it can’t really be considered accurate. But it is faithful. The format helps. This approach doesn’t often work, but it does here.)
• Cromartie High School
• Paranoia Agent
• Nerima Daikon Brothers
• Puni Puni Poemy
• Great Teacher Onizuka
• Gundam-San
• Oruchuban Ebichu

Depending on which flavor of weird one is going for, not all of these are going to scratch that itch.

• Flip Flappers
• Panty and Stocking
• Arakawa under the bridge
• Akiba’s Trip
• Seitokai Yakuindomo
• shimoneta
• Bakuon!!
• Ben-to!

asobi asobase is, imo, one of the funniest weird anime ever made

aho girl (be forewarned the anime ends on the creepiest fucking part of the manga)

azumanga daioh (be forewarned there is anime bullshit here as well, different time)

hinamatsuri (definitely well worth it to read the manga, which is one of the funniest I’ve ever read. It’s so good. The anime is great but it only got 1 cour which is an abridged version of the first 9 volumes. There’s 10 more and the story just keeps getting better), I felt like it was a bit of a spiritual successor to ranma which is also a good suggestion

Imo nichijou isn’t very good, though the animation is excellent. City was a much better manga and I’m excited to watch the anime for that. People love it though so it’s worth checking out

I genuinely enjoyed nokotan but the above picks all destroy it imo

Pop Team Epic. It was so weird I couldn’t get anything at all and dropped it in first 10 minutes, but I’m planning to give it another try someday 😅

Not really anime (but imo the anime version is worse): The way of the househusband.
Basically a Yakuza retires as a househusband.

Quite enjoyable

Y’all are all sleeping on Sarazanmai. Weird, but lives rent free in my head