Well, Naruto might gain a lot of power quickly. Orochimaru has a vast knowledge of jutsu and forbidden techniques. However, he would be in constant danger. Orochimaru could be using Naruto as a pawn for his own goals, like taking over Naruto's body. Also, the power Naruto gets might be unstable or come with a price, like draining his life force over time.
If Naruto goes to Orochimaru for power in fanfiction, it would be a huge shift in his character arc. He has always been against Orochimaru's ways. But if he does, he may find himself isolated from the people he loves. His relationships with Sasuke, Sakura, Kakashi, etc., would be severely strained. On the power side, he might learn some powerful and unique jutsu, but at the cost of his own integrity and the trust of others. And there's always the risk that Orochimaru's power could corrupt Naruto completely, turning him into a much darker version of himself, which would be a very interesting yet sad turn for his character.
In some fanfictions, Naruto might go to Orochimaru seeking power. He could be tempted by Orochimaru's knowledge of jutsu. Maybe he thinks that by learning from Orochimaru, he can become stronger faster and be better able to protect his friends and the village.
If Naruto was kidnapped by Orochimaru at birth, the entire Naruto universe would be drastically different. Konoha would lose its Jinchuriki, which could lead to a power imbalance. Without Naruto, the Nine - Tailed Fox's power couldn't be harnessed for the village's protection. Also, Orochimaru might have used Naruto's Uzumaki heritage and the power of the Nine - Tails for his own dark experiments. This could have led to the creation of more powerful and dangerous entities. His Akatsuki plans might also be affected as Naruto was a key part of their overall scheme.
When Orochimaru escapes in Naruto fanfiction, it often sets off a chain of events. His escape might inspire other villains to be more bold. Moreover, it can cause chaos in the world of ninjas. Younger ninjas may be sent on dangerous missions to track him down. And his escape could also mean that he has access to more forbidden knowledge, which he can use to further his own goals, whether it's immortality or world domination.
Perhaps Naruto goes to Orochimaru in an attempt to redeem him. Naruto has a strong belief in the good in people, and he might think that he can convince Orochimaru to stop his evil ways. He could offer Orochimaru a chance at redemption, like a new start in the Hidden Leaf Village if he gives up his dark experiments and ambitions. This would lead to a complex relationship development between them, with Orochimaru being skeptical at first but gradually considering Naruto's offer.
A plot twist might be that Naruto and Sasuke discover a hidden agenda Orochimaru has that involves someone they care about deeply. For example, they find out he's planning to use Sakura as a sacrifice for some dark ritual. This would force them to quickly come up with a plan to rescue her and stop Orochimaru once and for all.
His friends would be very confused and probably worried. They know Orochimaru as a dangerous and untrustworthy person. So, if Naruto starts acting like him, they might think something is seriously wrong with Naruto. For example, Sasuke, who has his own history with Orochimaru, would be extremely suspicious and might even turn against Naruto for a while.
One consequence could be that Naruto has some strange side - effects. Since Orochimaru's methods are often unorthodox, Naruto might have trouble controlling his chakra properly. For example, his chakra could be tainted with some of Orochimaru's dark chakra, making his jutsu less stable.
Since Orochimaru had many experiments and secrets, his death at Naruto's hands in the Chunin Exams fanfiction could lead to a scramble for his research. Other villages or even some rogue ninjas might try to steal his notes and facilities. In Konoha, Naruto might be pressured to reveal what he knew about Orochimaru's plans and secrets. This could put him in a difficult position as he may not know everything. Also, Sasuke, who had a connection with Orochimaru, might have a complex reaction. He could be angry at Naruto for killing Orochimaru, or he could see it as a sign of Naruto's strength and be motivated to become stronger himself.
The overall theme of the fanfiction could change. If Naruto absorbs Orochimaru, the story could start to explore themes like the nature of power and corruption more deeply. It might also delve into how Naruto can use Orochimaru's power for good, rather than succumbing to the evil associated with it. This could make the fanfiction more of a moral exploration within the Naruto universe.
It would likely become more complicated. Sasuke has his own history with Orochimaru. If Naruto goes to Orochimaru for power, Sasuke might see Naruto as a rival in a different way. He could be jealous that Naruto is getting power from Orochimaru, or he could be angry that Naruto is making the same 'bad' choice he once did.