What I'm about to say contains a lot of nonsense:
In Buddhism, "Hell" is the place where the sinned souls are sent to, and is believed to have 18 stages and each stage is used for different sin. So, I guess what Shikieiki judges shall be:
1. The sin you committed: the more sin, the more stage you have to be in.
2. The level of each sin: a repeated sin shall be considered "heavier", also your intention when committing the sin. This will tell how long you're gonna be in a stage of that sin.
Each sin has its own level, like murder is "more serious" than stealing, thus the torture is more painful. But heck, after I read all the stages' punishment they'll probably feel the same.
Surprisingly, I don't see anywhere states that regret can be considered. So when you arrive to the court, all you have to do is sitting there waiting for her judgement. You can cry, you can say sorry, you can promise but she won't care.
However.
It's impossible for a being to commit no crime in his/her/its life. Therefore after the sin, she will take a look at your deeds. Each deed has a level too, and they will cover up a sin at the same level (Like giving food to a beggar may cover up one stealing act, and saving one life can cover up one murder). After that, she will judge you.
1. If you still have sin: you go to Hell
ex: If Aya dies, and everything she did add up to Level 3 of Lying , she will be put in stage 5 for (I don't know how long, but one sin may get you 100 years). After that she may go to the Netherworld.
2. If you have nothing (no sin, no deed, or you did both equally): you go to the Netherworld
3. If you have deed(s): you go to Heaven
It gets a bit confusing here, about the Netherworld. It's supposed to be a waiting room, like Kisei said. However, this is also on the border. Netherworld connects to everywhere, and what you do here will greatly affect your next judgement. Yeah, don't think you've done with Yamaxanadu! Most people who did enough deed to cover their sins go there and have a peaceful time. You can say 90% of the population is elders who died of age. All they do is recall the past and stuff, yeah? But after a while, their memory fade, their souls rest and they disappear. No Heaven for them, they become one with nature, the Void. Also here, we have the sinners that survived their punishment in Hell. To be honest, I don't think it's possible to be sane after being in Hell, but some had very strong mind and made it. These guys usually committed the sin out of vengeance, the grudge was so strong it kept they sane. And thus we have ghost that haunt people around. Mima is very unlikely to be one of them, as she was boasting how she's a soul, but not a ghost. She could be strong enough to defeat the Shinigami after death, or cunning enough to trick them. Either way, I don't think Mima faced Shikieiki.
Ok, where were we? Oh, the Netherworld. Yuyuko lives there, very carefree. We all know she possesses the power of Death, which could be the result of a shitload of "sin". Her "murder" level can be off the roof, unintentionally or not. Additionally she suicided, and it's one of the great sins. However, she's not in Hell. Did Yukari do something? Maybe not, the answer I thought of lay under the Ayakashi. Yuyuko's past is uncertain, but I won't say it was a bright one. Yuyuko's corpse is buried under the Ayakashi and has a seal. This seal works with the requirement of Yuyuko's magic, thus make a connection between her soul and her body. Because of this, Yuyuko cannot be judged by a Yama nor she can be considered a soul. Shikieiki can put Yuyuko in Hell, but that will break the seal and release the Ayakashi's power. At this point, the Yamas chose to overlook her sins and make an alternative punishment: Yuyuko has to manage the Netherworld for all eternity.
Ah, I was talking about haunting ghosts tho... Ok, those ghosts (in The Ring, or The Grudge) after all those years in Hell, they try to go back to the living world from Netherworld. For what reason? Of course, because of the grudge, they're not satisfied, or the torture from Hell broke their minds, all they can think of is to go back to their old world, to do whatever kept them sane in Hell:
1. A memorial place: Most ghost stories you heard
2. A person: - to kill or to protect, either way because their mind is broken all they do is scare/harm the living.
3. Unfinished work: almost all of these works are murder-related
When they go back to this world, part of them haunt us for a while and disappear, as their sane is fading. Others keep doing it until they get exorcised or captured by the shinigami, then get judged again (this time it's 99% they'll go to Hell again). And... a few regain their consciousness, with their new ability as "soul", they likely to become youkai. Oh, and did I say what Yamas judged are not necessarily human-only? No? Well now you know. These souls can't do much to the living world, but they can "possess" a body, or an object, or even a material to trick the Shinigami (they only go for bodiless souls). Don't ask me how they then become a powerful youkai, I dunno. But since they know that they're soul, they have unlimited time to train themselves. The only problem is after they take a body, they will be forced to be compatible with it, eventually have a new life and forget about the past. This is only applied to the souls possess a living body, like human or animal.
These things are supposedly 10% of the youkai population. How do I know? I guess. There are a lot of theories on how a youkai was born, but I'm not typing it now.
'K, now Heaven. This is where the Elitists are. Basically just think of them like the Olympian Gods, who have nothing else to do than partying and having sex. This place is supposed to be where the "good guys" live. But like I said, Netherworld is the real "judgement". If you're a good guy there, you can go to Heaven. And when you're in Heaven, you can back to be a bad guy. Of course, at that time you can still be kicked back to Yama's Court, but if you don't get caught it's fine, no? Alrighty, what's the benefit of being in Heaven?
I'll use an old book, called "Journey to the West" as my reference. Heaven is a vast world above the sky, has 9 stages which are 9 layers of clouds. The highest is the Heaven Palace, where the King of Heaven lives. They have a lot of people, the Gods on the highest layers, the Celestial on the middle, and the Taoists on the lowest, where is about the top of the mountains. They have their leisure days up there, playing chess, drinking tea and debating on how bad Justin Bieber is. But the problem is Heaven itself. The environment is the best place to training one's self, both physically and mentally. They also provide high-quality food that make you more powerful. There are also pills that're mixed for a thousand years with godly craftmanship, guaranteed to give you godlike power/super long life. One of the most famous is the Peach of Heaven, I think you all know what power it holds, Tenshi is that strong cos she's been eating it since birth. There are a lot of tales about this fruit, but I already posted it last year. All the animals up there are as strong as an oni too, can you imagine how good is the meat?
So, basically if you're a good boy, you go to Heaven and train yourself until you're half as strong as Tenshi, you can go back to Earth and destroy a country. Sounds good, no? I think at that time even the Shinigami can't capture you. Thank god, Yamas' judgments are always right, and Hell's 18 stages are bad enough to break everything inside a living's brain, so we don't have many bad guys on Heaven. Most of them are just old farts who can't do anything but listening to Justin Bieber and playing chess.
Right, I'm off... I don't even know why I posted this, have a good laugh with my Asian myths rant... I'll come back soon with more nonsense.