There's also a possibility that Itachi would remain neutral for a long time. He would observe the different players in the Game of Thrones, much like he observed the events in the Naruto world. Only when he sees a real threat to the greater good would he choose a side.
Merlin could side with Jon Snow. Jon is a man of honor, much like Merlin himself. They both have a sense of duty towards protecting the realm. Merlin could use his magic to help Jon in his battles against the White Walkers, for instance, by creating magical barriers or enhancing the strength of Jon's army.
Theon Greyjoy also has his own side stories that are quite important. His time with the Ironborn and his struggle between his loyalty to his family and what he has learned from the Starks is really complex. We see his character development in a different light through these side stories.
One idea could be Itachi being a powerful sorcerer in the Game of Thrones world, similar to how he had powerful jutsu in Naruto. He could be part of a secret order that protects the realm from dark magic.
Cinderella would be a central figure. For the male lead, it could be a young and noble - hearted character like Robb Stark. He has the charm and leadership qualities similar to a prince. The stepmother could be a power - hungry noblewoman, like Cersei Lannister in some ways. The stepsisters could be her daughters, who are jealous of Cinderella's beauty and the attention she gets from the young lord. And then there could be other 'Game of Thrones' characters like Tyrion Lannister as a side character providing some wisdom and humor.
Daenerys could be a main character. She has leadership skills and her dragons could be a huge asset in a war - like scenario inspired by WWI. Another could be Jon Snow. His experience in leading the Night's Watch and fighting the White Walkers could translate into him being a key figure in this fanfiction's battles. Tyrion Lannister would also be a likely main character. His intelligence and ability to strategize would be very useful in a complex situation like a WWI - style conflict in Westeros.
He might ally with Arya Stark. Loki would see her determination and skill, and they could form an unlikely partnership. Arya could learn some new tricks from Loki's magic, and Loki could use Arya's knowledge of Westeros to his advantage.
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.
Arya Stark would be a great choice. You could write about her using her assassin skills to target key military leaders during the war. For example, she could infiltrate enemy camps disguised as someone else and take out important commanders, which would have a huge impact on the battles.
Arya Stark could be an interesting choice. Imagine if someone else transmigrated into her body. They would have to deal with her complex relationships, like her hatred for the Lannisters and her training with the Faceless Men. It would be a challenge to continue her story while also bringing in new elements from the transmigrator's personality or knowledge.
Definitely Tyrion Lannister. In a crossover with 'The Simpsons', he could bring his sharp wit and political acumen to Springfield. He'd probably outwit Mr. Burns in no time. His complex personality and ability to adapt would make for a very engaging character in such a crossover fanfiction.