Looking at these chapters, we are looking at a majority of the novel. Any summary will leave quite a bit of action out.
In these chapters, Huck and Jim encounter many characters from Buck Grangerford to Tom Sawyer, with many people in between. The significant episodes might be identified as the Grangerford episode, the Wilks episode and the Phelps episode.
In each of these situations, Huck encounters difficulty that places him in a position to make a difficult decision. With the Grangerfords, Huck agrees to help a young woman elope with her lover from a feuding family. With the Wilks family, Huck breaks his faith with the King and Duke (if he can be said to have been beholden to any bond of faith with them) and he informs Mary Jane Wilks that the King and the Duke are frauds. With the Phelps family, Huck decides to steal Jim out of captivity.
This summary leaves out the characters that play parts in each episode (the King, the Duke, Jim, etc.). In taking such a broad view we also leave out the lesser episodes that help to develop these characters, and Huck Finn, throughout the novel.