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.
The Lich King would bring an entirely new element to the political landscape. He has no allegiance to any of the Westerosi values or kingdoms. He might start by targeting the smallfolk, causing unrest among the people. This would then put pressure on the ruling houses. They would have to either try to fight him directly, which would be very difficult considering his powers, or find some way to negotiate with him. But negotiating with the Lich King would be like making a deal with the devil, as his goals are completely opposed to the survival and well - being of the people of Westeros.
Gunpowder can change the political landscape by giving an edge to those who possess it. For instance, a minor house with gunpowder can threaten larger houses and demand concessions. It could lead to new alliances being formed as houses seek protection from or access to gunpowder. Also, it might make traditional military strategies obsolete, forcing lords to rethink how they defend their lands.
She could be a key figure in uniting the Seven Kingdoms under a new form of government. Instead of the traditional monarchy, she might propose a council - based system where each kingdom has a representative. Her diplomatic skills and her family name would give her the credibility to bring all the kingdoms to the table and discuss such a major change.
If Sansa gives birth, it could solidify her claim to power in the North. A new heir means a continuation of her line, which would make it harder for any rival houses to try and usurp her position. Other regions might also view her differently. For instance, the Vale which has been an ally might become even more closely tied to the North. They could see the new heir as a way to further their own influence in the future of Westeros through marriage alliances.
The powers of the X - Men would have a huge impact. For instance, Jean Grey's telekinetic and telepathic powers. She could easily manipulate the minds of the lords and ladies, making them vote or act in a certain way. This would completely disrupt the normal political intrigue and power plays that are based on alliances and manipulation through words and gold. It could lead to a new form of rule where those with the most powerful mutants are in control.
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.
Kakashi could fit in as a foreign warrior. He could bring his ninja techniques which would seem like magic to the people of Westeros. His stealth and combat skills would make him a valuable asset or a feared opponent in the battles and power plays of 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.
Smaug could potentially be a part of the magical elements in the 'Game of Thrones' fanfiction. He could be connected to the old magic that once existed in Westeros. Maybe his presence awakens other dormant magical forces. His actions could also influence the political landscape. For example, if he attacks a certain region, the lords there would have to divert their resources from the power struggles to deal with the dragon threat, which in turn could give an advantage to other houses.
Legolas could be an outcast in the Game of Thrones world at first. But as he gets to know the people and their struggles, he decides to get involved. He could start a new movement, based on elven values like harmony with nature and loyalty. His actions could inspire characters like Jon Snow to think differently about leadership and ruling, and together they could work towards a more just and sustainable Westeros.
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.