Your original question did not meet enotes standards because of its lack of clarity and also because you actually asked more than one question - remember to just ask one, clear question per day! This will ensure that editors like me will get back to you with an answer soon! Anyway, I have edited your question slightly to make it clearer.
The majority of teachers use this excellent short story as a way of introducing students to the concept of situational irony: when we are led to believe that something will happen, only to find that something entirely different takes place. Situational irony is particularly effective because it reminds us that chance often has the last word and is a more powerful force than our plans. A question then to focus on in this short story is how is situational irony introduced in the story.
It is clear that in this story, then, the situational irony lies in the fact that both Dell and Jim have sold their greatest treasure to buy for the other something that they could use for their greatest treasure. Thus it is highly ironic that Dell sells her hair, but Jim buys her combs for her hair. Likewise that Jim sells his watch, but that Dell buys him a chain for that watch. Consider how Dell reacts when she opens the present that Jim has bought for her at such a cost:
For there lay The Combs - the set of combs, side and back, that Della had worshipped for long in a Broadway window. Beautiful combs, pure tortoise shell, with jewelled rims - just the shade to wear in the beautiful vanished hair. They were expensive combs, she knew, and her heart had simply craved and yearned over them without the least hope of possession. And now, they were hers, but the tresses that should have adorned the coveted adornments were gone.
This is the true situational irony in this tale that makes it so successful and so unforgettable. As the narrator comments in the final paragraph, although some may view their actions as "unwise", actually, through their motivation of showing love to each other and giving up their finest possession for the other, they have shown themselves to be "the Magi", through the situational irony of the tale.