Most of the post-game of Disgaea 5 (and all Disgaea games, I believe) is the Carnage Dimension maps. This should take significantly more time than the main quest due to the insanely steep ramp up of enemy strength. Hardcore Disgaea fans would probably say that the real game is the post-game and that the "main" game is mostly tutorial.
Plot wise, there are some questions from the main game that are answered. I am not sure how invested in plot you are, but I think it would be accurate to say that the post-game is gameplay-centered, rather than plot-centered.
As for the DLC stages, they are completely unrelated to the story at all, but they do get you main characters from past Disgaea titles.