They could use magic to disguise themselves. For example, Hermione is very skilled at the Polyjuice Potion, so they might use that to change their appearances. They would also need to be careful with their magic use to avoid detection by the Ministry's trace. Maybe they would use non - traceable magic like some ancient spells that are not well - known.
They could use disillusionment charms constantly to blend in with their surroundings. This would make it difficult for Voldemort's forces to spot them. Also, they might use the Marauder's Map if they manage to get hold of it. It would help them avoid any approaching Death Eaters or other threats.
Maybe he gets help from his friends. For example, Ron and Hermione could come up with a plan. They might send him a magical object that can help him escape, like a flying broomstick that he can use to fly away from the Dursleys' house without being noticed.
Grace compares catching the cat to "catching air: impossible." The cat's supernatural agility exceeds normal feline capability, reinforcing the theory that it's a magical being rather than an ordinary animal.
Maybe they run away because they are tired of the constant danger at Hogwarts. They've faced so many threats, and they just want a break. So they run to a peaceful place where no one knows them.
One challenge could be finding a safe place to stay. The wizarding world is not that big, and there are many places that are easily detectable. They would need to use magic carefully to avoid leaving a trail for those who might be looking for them.
Another plot could be that they run away to escape the chaos and danger at Hogwarts during a particularly bad time, like when Voldemort is really tightening his grip on the wizarding world. They set out to find allies outside of Hogwarts, like some old and forgotten wizarding families, and together they form a resistance against Voldemort.
In a 'Harry and Hermione run away fanfic', they could be running away from the pressure of their pre - destined roles. Harry is always seen as the 'Chosen One' and Hermione as the brilliant sidekick. Fed up with these expectations, they decide to run away and explore the wizarding world on their own terms. They might travel to different wizarding schools across the globe, learning new spells and making new friends outside of Hogwarts.
Loki could enlist the help of some unlikely allies. For example, he might strike a deal with a creature from the realms outside of Asgard. In exchange for a future favor, this ally helps him escape by providing a means of transportation or a way to bypass Asgard's defenses.
Some fans like it because it offers an alternative to the canon relationships. It gives a chance to explore a different dynamic between Harry and Hermione, one that might be more romantic or at least a very deep friendship that's different from what's shown in the books. It allows for creativity and new storylines.
In the fanfiction, Harry could outsmart Hermione by understanding people better. Hermione is often very logical and book - smart, but Harry might be more in tune with the emotions and motives of others. He could use this to his advantage in a situation where they are trying to solve a mystery or deal with a difficult person. He can read between the lines and make decisions based on his gut feeling about people, while Hermione is still analyzing the facts from her books.