Because all three stories mentioned above exhibit many of the defining elements of O. Henry's work, there are more similarities among them than there are differences. 

All three stories display the following similar qualities: 

—Typical settings and the use of "local color"

O. Henry's stories are often set in New York City as are "The Last Leaf" and "The Gift of the Magi." Other typical settings are the West and the South, in which "The Ransom of Red Chief" is set. In all of these stories, there is "local color." For instance, O. Henry employs the speech patterns of the common folk of the settings. Such usage adds realism and interest to the narratives.

In "The Last Leaf," the accent of Mr. Behrman adds a quaint touch to this character, and in "The Ransom of Red Chief," the dialect of Sam and Bill suggests that they are not much better educated than the "yokels" of the town that Sam ridicules. This similarity assists the realism and humor of the stories.

—The theme of the unexpected quality of life 

In "The Gift of the Magi," the James Dillingham Youngs have seen a reduction in their income, and because of this situation, neither Della nor Jim has money with which to purchase a Christmas gift. When the young husband and wife make personal sacrifices to buy a gift for each other, the result of their generosity is completely unexpected.

In "The Last Leaf," Johnsy says she will die when the last ivy leaf falls from a vine she sees outside her window. After trying everything that she can think of to motivate Johnsy to live, Sue despairs of believing that the last leaf on the ivy vine will not fall off in the bitter cold as the others have done, and that Johnsy will regain her will to live. However, during the night Old Behrman makes the ultimate sacrifice so that Johnsy will be encouraged to fight to live when she sees that the ivy leaf is apparently still on the vine the next morning.

In the humorous story, "The Ransom of Red Chief," much is unexpected. The two kidnappers, Sam and Bill, are convinced that the people of Summit, Alabama, will be easy to exploit. However, Ebenezer Dorset outsmarts them, and his son that they kidnap terrorizes them. These unexpected circumstances certainly affect the men as they receive no ransom money; instead, they must pay Mr. Dorset to take back his wild and unruly child.

—The ironic reversal

All three stories have a surprise ending. In "The Gift of the Magi," Jim and Della have unselfishly sacrificed their most prized possessions so that they can purchase gifts for each other. Unfortunately, the Christmas gifts that they give each other are for those sacrificed possessions. In "The Last Leaf," there is one ivy leaf which has not fallen. Seeing what she believes is a tenacious leaf, Johnsy decides that she wants to live after all. Unfortunately, Johnsy and Sue later learn that Mr. Behrman has gone out into the frigid weather to paint a leaf on the building's wall that Johnsy would be sure to see. Further, the little man subsequently dies from pneumonia. Finally, in "The Ransom of Red Chief," Sam and Bill are, ironically, the ones who pay a ransom, not the father of Red Chief. And, they leave Alabama poorer, not richer, for the experience.

—There is a distinct difference in the tone and theme of one story from the other two:

While there is a romantic quality to "The Gift of the Magi" and "The Last Leaf," the rather satiric humor of "The Ransom of Red Chief" differs from the others in tone as the character of Sam is apparently ridiculed.

Love and true friendship are developed as themes in "The Gift of the Magi" and "The Last Leaf," but in "The Ransom of Red Chief" Sam allows his supposed friend Bill to be terrorized by the wild child of Ebenezer Dorset. In one of the last incidents of Red Chief's terror, Sam hears Bill screaming as Red Chief prepares to scalp Bill. While he does get the knife away from the boy, Sam seems rather unsympathetic and selfish:

Just at daybreak, I was awakened by a series of awful screams from Bill. . . .
It's an awful thing to hear a strong, desperate, fat man scream incontinently in a cave at daybreak.

Shortly after this incident, Sam gets up before dawn because he remembers that Red Chief has declared that he is to be burned at the stake "at the rising of the sun." Sam denies that he is afraid, but he selfishly leaves Bill to his own devices as he claims that he needs to "go up on top of this mountain and reconnoiter."

What are the differences among "The Last Leaf," "The Ransom of Red Chief," and "The Gift of the Magi" by O. Henry?

The differences between these stories are many.  "Red Chief" is a comedy for the most part, "The Last Leaf" is a rather sardonic tradegy, and "The Gift of the Magi" is more of a touching tale of a couple's love.  Chief is set in the old west with two outlaws, Leaf is in Greenwich Village in the early 1900's and is about two female roommates and an old man, and Magi is set in a town in an unknown time period and is about a young couple.  So even the settings and characters are diverse and varied.  Chief doesn't really have a moral or lesson, that is super obvious or serious anyway.  Leaf does have a moral of unappreciated love or effort, and Magi has a very blatant theme of sacrifice and love.  The stories even have a different feel to them.  Chief is humorous, witty, and focuses less on a judgment of the characters and more on simply telling the tale in a humorous way.  It is also in first person.  The other two stories are in third person, and Leaf has a strong feeling of rather critical judgment of the people in the story; one senses O. Henry finds them shallow and unappreciative.  In Magi, it is also in third person, but less judgmental; it is more a simple retelling of events.

I hope that thoes thoughts help to get you started; good luck!  They are all great stories!