A possible plot could be that the Hunger Games are a new form of ninja training in a distorted future. Naruto enters the games not fully understanding what they are about. As he progresses, he discovers the dark secrets behind the games. He then uses his chakra and his ability to inspire others to lead a revolt against the people running the Hunger Games, similar to how he always stands up against injustice in the Naruto world.
I think Rock Lee could survive. His physical strength and speed, along with his determination, would serve him well. Also, Shikamaru. Despite not being as physically strong as some others, his high intelligence would enable him to outwit his opponents and avoid dangerous situations in the Hunger Games arena.
One popular idea is a Hunger Games crossover with Harry Potter. Imagine tributes from the districts having magical abilities or facing challenges in the arena that are magically enhanced. Another is a crossover with The Maze Runner, where the tributes find themselves in a maze - like setting within the Hunger Games arena. A third could be a crossover with Divergent, with the factions being incorporated into the districts and the Hunger Games having different rules based on the faction - like qualities of the tributes.
It could be really interesting. Imagine the characters from Glee suddenly thrust into the brutal world of the Hunger Games. The singers and performers from Glee would have to use their wits and any hidden survival skills. For example, Rachel Berry might try to use her show - stopping voice to gain sponsors, much like the tributes in the Hunger Games do to get supplies. And the different cliques in Glee could form alliances similar to the district alliances in the Hunger Games.
It could be really exciting. Imagine Harry Potter characters in the arena of the Hunger Games. Maybe Harry would use his magic skills to survive, like creating protective spells against the various threats in the arena. Hermione could use her intelligence to strategize, similar to how tributes in the Hunger Games plan their moves.
Four is also quite popular. His leadership and training abilities could potentially change the dynamics of the Hunger Games. He might be the kind of character who could organize an underground rebellion within the arena, much like he did in Divergent with the factionless.
First, you need to decide which two universes you want to cross over. For example, if it's Hunger Games and Game of Thrones, figure out how the political intrigue of Game of Thrones can be incorporated into the Hunger Games world. Then, think about your characters. Will they be a mix of existing characters from both universes or new ones? Next, create a basic plot. Maybe the tributes in the Hunger Games are being influenced by the power struggles in the other universe. Finally, start writing, don't worry too much about making it perfect at first.
It could be really exciting. Maybe Percy and his demigod friends get thrown into the Hunger Games arena. Percy could use his water powers to his advantage, like creating water barriers or using water currents to move around quickly. The demigods' unique abilities would make for some very interesting battles against the regular tributes from the Hunger Games.
A possible plot is that the Capitol in the Hunger Games discovers the existence of vampires from Twilight. They see them as a new form of entertainment and try to capture them to put in the arena. However, the vampires are not so easily controlled. Katniss and her allies could team up with the vampires against the Capitol. This would bring together the themes of rebellion from Hunger Games and the supernatural elements of Twilight.
In a crossover, the angels and demons from Supernatural could be interested in the Hunger Games as a form of entertainment. Castiel could send Dean and Sam to the Games to stop an apocalypse that is predicted to start there. The boys would have to blend in as tributes, learn the ways of the Games, and figure out which of the other tributes are being influenced by the supernatural beings pulling the strings behind the scenes.