The narrator of Twain's tale believes that the box he is transporting contains the body of an old friend that he is excorting home. What he does not know is the the box containing the body was accidentally switched with a box of guns being shipped. Also, a hobo had jumped into the boxcar and set a bag that contained Limburger cheese on top of the box and then left. The cheese smells horrible, and both the narrator and the conductor attribute the smell to the body they believe is in the box. They go through all kinds of outlandish ways to cover up the smell, including burning trash, but the heat from the fire only melted the cheese, making the train car stink even worse. The narrator ends up getting very ill from sitting outside on the back of the train car in the cold to avoid the smell when all they had to do was investigate and throw out the bag containing the rotten cheese.
There are a number of cases of irony in the Invalid. But to name two that stand out to me, is 1: Limburger cheese is best if kept in the cold. The men are lighting a fire and warming up the railway car not knowing that they are making it worse. By the end of the story, the cheese is in the warm car and the men are out in the cold. 2:The narrator of the story is taking his final trip home to die, on a train. The cause of his demise is that he was on a train taking a dead body back to it's final resting place