Castiel's stoic and somewhat naïve personality in Supernatural would contrast with the more worldly and sly characters in Good Omens. However, his loyalty and sense of duty could be something that the Good Omens characters would admire. And in return, the Good Omens crew could teach Castiel to loosen up a bit and not be so rigid in his thinking.
The powers of the Supernatural characters, like Sam's psychic abilities and Dean's combat skills, would contrast with the more otherworldly powers of the Good Omens characters. Aziraphale's ability to perform miracles and Crowley's demonic powers would be on a different scale. For example, Sam's psychic visions might be able to predict events that Aziraphale and Crowley are involved in, but they might not fully understand how he gets these visions at first.
Another great storyline could involve the prophecies in Good Omens intersecting with the apocalyptic events in Supernatural. The characters from both would then be scrambling to prevent or at least manage the impending doom. The Horsemen from Supernatural might interact with the Horsemen - like figures in Good Omens, leading to a battle of wills and powers that would keep readers on the edge of their seats.
One idea could be that Sam and Dean from Supernatural get thrown into the world of Good Omens. They team up with Aziraphale and Crowley to stop a demon from opening a portal that would unleash all kinds of chaos. The Winchesters' hunting skills combined with the angel - demon duo's knowledge of their own universe could make for an exciting adventure.
The New Girl characters have very distinct personalities. Jess is the idealistic dreamer, always seeing the best in people and situations. In a crossover with Percy Jackson, this could lead her to trust the wrong characters at times, but also to befriend some of the more misunderstood creatures. Nick's laziness might be a problem when it comes to the physically demanding tasks in the Percy Jackson world, but his loyalty to his friends would shine through. Schmidt's competitiveness could either make him a great ally in battles or cause him to make hasty decisions. And Winston's love for animals could potentially lead him to form an unlikely bond with some of the mythical beasts in the Percy Jackson universe.
Well, Shawn from Psych is really outgoing and a bit of a show - off, while the BAU agents in Criminal Minds are more reserved in their own ways. In fanfiction, it can be really interesting to see how Shawn's antics either annoy or amuse the Criminal Minds characters. For example, Derek Morgan might be initially frustrated by Shawn's non - traditional methods but then come to respect his insights.
One way to create an engaging plot for this crossover fanfiction is to focus on the characters' reactions to the new world they find themselves in. Imagine Dean Winchester suddenly in the middle of London and being confronted by an angel and a demon who don't quite act like the ones he's used to from his own world. His confusion and initial mistrust could lead to some interesting dialogue and action scenes. Sam, on the other hand, might be more open - minded and start asking questions about the Good Omens universe. Meanwhile, Aziraphale and Crowley are trying to figure out who these strange American hunters are. This interplay between the characters from different universes can drive the plot forward.
Well, Superman's strength and invulnerability would be a great match against the brute force of some of the larger Warhammer creatures like Ogres or even some of the daemons. His heat vision could also be a useful weapon against hordes of enemies. Batman's strategic mind would be invaluable in dealing with the complex politics and power struggles in the Warhammer universe. He could also use his gadgets to adapt to the different technologies and magics there. Wonder Woman's combat skills and her Lasso of Truth could be used to great effect in dealing with the more devious characters in Warhammer, like the Dark Elves.
One interesting pairing could be Dean Winchester and Crowley. Dean has a lot of experience dealing with demons in the Supernatural world, and Crowley has his own unique charm and deviousness. Their interactions would be full of witty banter and power plays. Another pairing could be Sam Winchester and Aziraphale. Sam is the more intellectual of the Winchester brothers, and Aziraphale is an angel with a vast knowledge of the cosmos. They could have deep conversations about morality and the nature of good and evil.
One plot idea could be that Aziraphale and Crowley from Good Omens get dragged into a case that the Winchester brothers are investigating in Supernatural. Maybe it's a demon that's a bit too powerful for Sam and Dean, and they need the help of the angel and demon duo who have a different approach to dealing with the supernatural. Another idea is that the two universes' versions of Heaven and Hell start to merge, and characters from both shows have to figure out how to stop it while also dealing with their own personal issues.
In a crossover, Lucifer from 'Lucifer' might become more hardened in the 'Supernatural' world. The constant danger and the presence of hunters like the Winchesters could make him more cautious. He might also have to tone down his flamboyant side a bit to fit in. As for the Winchesters, they would be extremely wary of Lucifer at first. Dean especially might be more aggressive towards him initially, seeing him as just another devil to slay.