It's changed a lot over the years. It's mostly been carried on the backs of many, many different artists that come and go every few years. There's never really a central story or anything for them, mostly loose folklore. Here's a list and their wiki-pages for more reading.
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Heyuri-tan has been the poster child ever since she was made in i think 2021, and obviously recieved most of the OC cuz of that. - https://wiki.heyuri.net/index.php?title=Heyuri-tan
Iruyeh-tan is the evil troll sister with sad backstory. She hasn't come around in a little while. I miss her. - https://wiki.heyuri.net/index.php?title=Iruyeh-tan
Kaguya is... Kaguya. The admin. depicted as Kaguya Houraisan from touhou. (i like to call him kaguya-abi in my mind. the wiki page isn't that relevant)
/q/-tan is one you might see less often. I think she's cute. - https://wiki.heyuri.net/index.php?title=/q/-tan
faganon is a fat red guy. Usually associated with an annoying guy that i dont think posts here anymore, but is an umbrella annoying guy of Heyuri. - https://wiki.heyuri.net/index.php?title=Faganon
Puchippy is a character from Di Gi Charat. Her actual name is Puchiko, but back in September 2024 we had her as the mascot of a clippy like assistant that watched out for Rule 8 words when you made posts. It was annoying so we got her kicked out, but we keep calling her puchippy from that event. - https://wiki.heyuri.net/index.php?title=Puchippy

Waha is typically associated (here) with anonwaha, the admin of CGI@Heyuri and mod. Yamato Suzuran and Waha is its own, japanese internet meme. - https://knowyourmeme.com/memes/yamato-suzuran-waha

You'll generally see alot of japanese internet memes in OC.

Some of the characters you might see in older OC:
Hatsune Miku - This is lolico, the founding admin. Don't see her as much anymore since he left about 3 years ago - https://wiki.heyuri.net/index.php?title=Lolico
Tokino Tomo - This is kuz, the other admin. More recent and was around for stuff like the Golden Age of Heyuri and also a bit of a drama magnet. Led to quite a bit of the OC and stuff you see today though. https://wiki.heyuri.net/index.php?title=Kuz
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The wiki page for OC is a little outdated, but it's still nice if you wanna have a look for a bit of the old stuff. - https://wiki.heyuri.net/index.php?title=Original_content