Typically, they use some sort of magical or dimensional rift to merge the two worlds. For example, Naruto could be sucked into a portal that leads him to the High School DxD universe. Or, it could be a more complex plot device like a powerful villain trying to combine the two worlds for their own gain.
One way is through a shared enemy. The fanfiction might introduce a new threat that both Naruto's world and High School DxD's world have to face together. This forces the characters from both universes to interact and cooperate. Another way is through a character's unique ability. Maybe a character in Naruto has a power that can open a gateway to other dimensions, and they accidentally open it to the High School DxD world. This then starts the process of the two worlds coming together and the characters having to deal with the consequences.
The power systems might also clash. In the Naruto world, power often comes from training and mastering one's own internal energy. In High School DxD, it's more about the power of the Devils, Angels, and Fallen Angels. So when Naruto enters the DxD world, his idea of power through hard work might be at odds with the more innate powers of the DxD characters. He could try to teach them his ways, or they could try to convince him that their powers are superior.
The orphan could rely on their adaptability. Since they are used to being alone, they might be more open to learning the new rules of both worlds. In the Naruto world, they might have learned to be resourceful, and they can apply that in High School DxD. For example, using their knowledge of chakra to understand and maybe even manipulate the magic in High School DxD.
One way is through the power systems. Naruto's chakra could interact with the magic and powers in High School DxD. For instance, a character from High School DxD might be fascinated by Naruto's ability to use chakra and it could be a starting point for a relationship in the mass harem. Another aspect could be the cultures. The shinobi culture of Naruto's world is very different from the high school and supernatural culture of High School DxD. This contrast could create interesting situations in the fanfiction.
One way is through the concept of power transfer. For instance, a character from Naruto could accidentally gain the power of a devil in High School DxD and have to figure out how to control it. This would lead to some really cool action scenes as they struggle with the new power. Another way is through cultural exchange. The shinobi culture from Naruto could be introduced to the High School DxD characters, creating some interesting interactions.
Yes, there are some. You can start by looking on fanfiction platforms like FanFiction.net or Archive of Our Own. Some authors create crossovers where Naruto characters interact with the High School DxD universe in a platonic or adventure - based way. For example, they might have Naruto and his friends visit the DxD world to help with a demon - related problem, without any inappropriate content.
Another possibility is that there is a tournament that spans multiple universes. Naruto is selected to represent his world, and Rias volunteers or is chosen to represent the High School DxD world. They meet at the tournament grounds. At first, they might be a bit suspicious of each other, but as they see each other's skills and determination in the battles, they start to respect and eventually become friends, working together to win the tournament for their respective worlds.
Another way is through a powerful artifact. Suppose there is an ancient artifact in Highschool DxD that has the power to connect different dimensions. When it is activated, it links to the world of Overlord. This could lead to all sorts of storylines, like characters from both sides trying to control the artifact for their own purposes, or working together to keep it from falling into the wrong hands.
The merge can also happen on a more conceptual level. For example, the idea of friendship and teamwork, which are important in both series, could be the connection. Naruto's belief in his friends and the Digidestined's bond with their Digimon could be seen as similar. This similarity could be the starting point for the two worlds to interact in fanfiction. Writers might have Naruto and the Digidestined team up to fight a common enemy that threatens both the Digital World and the ninja world. They would combine their unique powers and skills to achieve victory.
Well, in a popular one called 'Naruto's New Realm', Naruto discovers a portal that leads to Rias's world. As he steps through, the two worlds begin to merge in a way that combines the ninja techniques with the demonic powers of Rias's realm. It's really cool to see how the two different power systems interact and how the characters from both sides deal with the new situation.
In some fanfictions, the merge happens when a powerful artifact from either universe is activated. This could be a Kamen Rider's belt or a powerful relic from Highschool DxD. When this happens, it creates a rift that pulls elements from one universe into the other. The characters then have to deal with the new and unexpected situations. For instance, the devils in DxD might be intrigued by the Kamen Rider technology and try to harness it for their own purposes.