What is the ruling on reading English stories to strengthen language skills and for entertainment, while avoiding parts that describe inappropriate matters between characters?

The basic principle is that it is permissible to learn English and other foreign languages, as long as it does not lead to something forbidden. Reading or listening to pornographic stories is not permissible, due to the immorality, vice, and depiction of indecency they contain. A Muslim must restrain their sight and hearing from all vice and indecency.

If the stories you are asking about do not contain anything prohibited, or if you avoid that content when reading, then there is no harm upon you.