One interesting crossover could be a battle scenario where Natsu's fire - based powers from Fairy Tail are pitted against the devils in Highschool DxD. His dragon slayer magic might give him an edge against some of the lower - level devils.
Another place to check is Archive of Our Own (AO3). It has a large collection of fanfictions. When looking for Highschool DxD and Natsu Dragneel crossovers there, make sure to read the tags carefully. Tags can give you an idea of what the story is about, like if it's more action - based, or if it focuses on character relationships. Some fanfictions might be a mix of both, and those can be really engaging.
Well, one possible plot could be that Natsu is betrayed in his own world and somehow ends up in the DxD Highschool universe. Maybe he has to deal with the different power dynamics and politics there while also trying to figure out who betrayed him in his original world. He might form new alliances with the characters in DxD Highschool and use his unique abilities to survive and seek revenge for his betrayal.
One idea could be a crossover where Natsu finds himself in the world of High School DxD and has to deal with the devils and angels there. He might use his fire magic in unique ways to combat the various threats in that universe.
Well, I'm not sure how widespread it is, but it's possible to find such fanfiction. Writers often like to mash - up different universes to create something new. In a 'Harry Potter is Natsu Dragneel' fanfic, you might expect to see Harry with Natsu's determination and love for his friends translated into the context of the wizarding world. Maybe he'd be more brash and use his 'fire - like' magic in a more aggressive way like Natsu does.
A common plotline is the rescue mission. His friends from Fairy Tail band together to find and save him. Another is Natsu trying to break free on his own. He might use his fire magic in creative ways to escape his bonds.
Perhaps Natsu's presence could disrupt the balance between the three factions in the Highschool DxD world. His strong sense of justice might lead him to oppose some of the more underhanded dealings among the devils, angels, and fallen angels. This could start a chain of events where he has to prove himself and his beliefs to the various characters.
Natsu, being a fiery and passionate character, would likely have a rather intense interaction with the DxD Highschool characters. He might be initially distrustful due to his recent betrayal. But some of the more friendly characters in DxD, like Issei's group, could try to befriend him. Natsu would probably show off his powers a bit, which would either impress or intimidate the others. And there could be some clashes in personalities, for example, Natsu's straightforwardness against some of the more devious DxD characters.
Incorporate some mystery elements. Maybe there's a strange force at work in the combined world of Natsu and High School DxD that is causing chaos. Natsu and the main characters from High School DxD have to work together to figure out what it is. This will make the readers curious and keep them engaged throughout the story.
It could be another male character who is also interested in the same person as Natsu. This would create a love triangle. He might be from a different guild or have a different type of magic, and the competition between him and Natsu for the girl's love would be a major part of the story.