The hotel, or more specifically the *spoiler*, translates all languages into the native language of the listener... Do people and mythicals still have accents?

More importantly does Asterion have an accent, and if so what is it? Or would his accent be fairly neutral from having been exposed to hundreds of accents across many hundreds of years?

At times through the story, accents are mentioned, namely in later chapters. It would be safe to presume that accents still apply, relative to your original language. I'm unaware of any examples of spoken ancient Cretian language currently, but I presume Asterion would have a Greek accent, if only due to lack of ancient Cretian examples.