“Botan here! I'm popping in to give another wonderfully helpful explanation of the world Yusuke and his friends inhabit! This time, I'm talking about yokai. You know them as 'demons' or some variant of that if you watched the dubbed anime! They're creatures from Japanese mythology that take all sorts of forms. Yes yes, it's all quite intriguing, so why don't you give the table below a go~?”
Yuusuke Yuurei
When Yuusuke dies he becomes a ghost for a short while, but the traits of this form line up with the traditional depictions of Japanese ghosts, caled Yuurei (幽霊), Obake, or Shiryou. Human souls are supposed to pass on peacefully after a proper funeral, but those who have unfinished business or die suddenly can be anchored to the living world, still seeking to make right what they need. He is sometimes depicted with a triangle headband as well, signifying his ghastly nature.
Botan Shinigami / River Sanzu
Shinigami (死神) are closer to apparitions than to gods (signified by "kami/gami"), but Botan is certainly much nicer in appearance and behavior. Shinigami are often horrific monsters attracted to death and who will continually possess humans in an area for murder after murder until ritual purification can take place. I guess Botan is just attracted to death by job description? Her main role though is as a guide across the River Sanzu, a location in Buddhist myth where good souls can cross over with a bridge into the afterlife safely, and the evil are thrown in the rapids below to be devoured by dragons. The English dub describes Botan as the ferry girl of the River Styx, a similar location in Greek mythology leading to the Underworld and ferried by a figure named Charon.
Koenma and his Father Enma-Daiou / Yama
Again, a Buddhist figure rather than a yokai, Enma (閻魔) is the king of the Underworld and is the figure who judges whether a soul will go to heaven or hell when they die. He is very mysterious, but most legend makes him out to be feared. He is said to have been the first person to die, and his punishments are swift and painful. Koenma has a lot to live up to...
Jorge Saotome / Ogres Oni
Oni (鬼) are a common type of yokai, commonly translated as orges in English. They are brutish creatures, often with bright red, blue, or yellow skin who wear animal pelts like a tiger. They are often found terrorizing humans or eating them, and seem to revel in human suffering. They are typically stock villains in old myths and aren't all that smart.
Kuwabara Mulberry / Ward
Not a creature, but a superstition. Kuwabara (桑) refers to the Mulberry tree, an important tree throughout the world but partically Chinese and Japanese folklore. They are believed to never be struck by lightning, and repeating the phrase "kuwabara kuwabara" is said to ward off evil spirits.
Three Artifacts of Darkness Imperial Regalia of Japan
Rooted in the mythology of ancient Japan, the Three Artifacts are based directly on these items used to enthrone the oncoming Japanese Emperor. They include the sword Kusanagi no Tsurugi (草薙劍), the mirror Yata no Kagami (八咫鏡), and the jewel Yasakani no Magatama (八尺瓊勾玉).
Kurama Kitsune
Hiei Jagan Eye / Evil Eye
Gouki Kyuukonki
Four Saint Beasts Four Guardians of the Compass Directions
Yukina Yuki-Onna