Maybe he could be a foreign knight who arrives in Westeros. He hears of the chaos and decides to bring his own brand of justice. He starts by helping the smallfolk and gradually gets involved in the bigger power struggles, using his swordsmanship and leadership skills.
The Hulk might be seen as a sort of monster in the context of Game of Thrones. Just like how they have direwolves and dragons, the Hulk could be another mythical - but in this case, suddenly very real - creature. He could be shunned by some and perhaps worshipped as a god by others, depending on how different regions of Westeros react to his existence.
Danny could be a mysterious figure that arrives in Westeros. He might be mistaken for a wizard or a demon at first. His powers would make him a force to be reckoned with. For instance, his invisibility could be used to spy on the different houses. He could then use the information he gathers to either help the good guys or play his own game.
The God OC could be an ancient being that has been slumbering for ages. In the fanfiction, something could awaken this God OC, like the excessive use of dark magic. Once awake, they start interfering in the affairs of Westeros. They might side with certain houses based on their own motives. For instance, if they value honor, they might support House Stark. Or they could be a more neutral force, only interested in maintaining a balance of power in the world. They could use their divine powers to stop any one house from getting too powerful, like preventing the Lannisters from completely dominating the Seven Kingdoms.
In fanfiction, Aragorn could potentially be a king from a far - off land who arrives in Westeros. He might bring with him a different style of leadership and a sense of honor that is somewhat different from the lords and ladies of Westeros. He could get caught up in the power struggles, especially if he realizes the threat of the Iron Throne being misused. Maybe he would try to form alliances with the more noble houses to bring stability to the land.
She could fit in as a spy. Given her ability to deceive and her immortality, she could gather information for different factions. For instance, she could work for the Starks initially, but then switch sides if she saw more benefit elsewhere.
Fem Harry can fit in by being an outsider with unique powers. Just as she was an outcast in the wizarding world at first in Harry Potter, she could be in Game of Thrones too. Her magic would set her apart from the regular characters, and she could use it to either help or disrupt the existing power dynamics. For instance, she could use her ability to communicate with animals to gather intelligence in the cut - throat world of Westeros.
They could be a new faction. Samurai have a strict code of honor, much like the knights in Westeros. They might be seen as a threat initially, but could also form alliances. For example, they could side with the Starks who also value honor. Their unique fighting styles would be a novelty in the battles of Westeros.
The Lich King could be a major disruptor. He doesn't care about the normal politics of the Iron Throne or the houses. He would likely try to use the political chaos to his advantage. For example, he could support one side in a war just to create more death and destruction, which he can then use to raise more undead soldiers.
A house gardener could fit in as a keeper of secrets. The gardens often have hidden corners and old trees that could hide things. He might stumble upon a hidden cache of weapons or a secret meeting place. His presence is often overlooked as he is just a gardener, so he can observe a lot without being suspected.
Some fanfics make vampires fit into the GoT world by having them be related to magic. Since there is already magic in the GoT universe, vampires could be a part of that magical ecosystem. Maybe they were created by some dark magic long ago and are now starting to surface as the magic in the world becomes more prominent again. They could have unique powers that interact with the existing magical elements in the story, like being able to resist the warging ability of some characters or having an immunity to certain poisons because of their undead state.