"The Last Leaf" by O. Henry is less funny and entertaining than other O. Henry stories, but it still carries a sarcastic tone that shadows much of it; it's like he is telling the story but not quite taking it seriously himself. He makes a bit of fun of the residents of the neighborhood that the story is set in, Greenwich Village. He writes:
"So, to quaint old Greenwich Village the art people soon came prowling, hunting for north windows and eighteenth-century gables and Dutch attics and low rents. Then they imported some pewter mugs and a chafing dish or two from Sixth avenue, and became a 'colony.'"
So, the story starts off with that rather bemused and sarcastic tone, which he keeps a thread of throughout the entire story. But, the mood turns a little bit more serious as he describes how Johnsy is hit by pneumonia. So, he has introduced a very serious illness into a story that started off as satirical; do we take the piece seriously, or with amusment? It's a rather odd combination that continues throughout the entire piece: he introduces characters through insults and sarcasm, then asks us to care about those characters when bad things happen to them.
I provided links below to further discussions of the style and characters, and that should help a bit too; good luck!