John Steinbeck is a very clever writer. Hence, he uses irony in his book in various ways. Some of them are clear and in your face; others are subtle. 

One of the clear uses of irony emerges right way.  Steinbeck gives the biggest man in the book the name of Lennie Small. There is nothing small about Lennie. He is a hulk of man, and he shows it in the fields as he works and when he crushes Curley's hand in a fight. 

Another clear use of irony can be seen in Curley's wife. She comes onto all the men and she is attractive, but all the men turn her away and shut her down. 

A more serious use of irony is the death of Lennie. When Lennie accidentally kills Curley's wife, George knows that the only fate left for Lennie is a slow death by an angry mob of men.  Therefore, as his best friend, he has to find Lennie before the others do. When he finds him, he tells him the story of how they will live off the fat of the land and then he shoots him in the head. George's love and loyalty to Lennie made him take his life. This type of irony can only make the reader shed a tear at the hardships of migrant workers. 

Also I should say that not all ironies are created equally. Some are funny, others are clever, and still others are tragic. 

There are lots of examples of irony in Steinbeck's novel, but the most glaring one is the fact that George must kill Lennie because he loves him.

It is a heart-wrenching scene. Lennie thinks, in his naive, child-like way, that he and George are finally going to get the land with the rabbits for him to tend. Instead, George must kill him. He does so because there is no choice. It is either kill Lennie humanely and quickly or watch as the brutal posse tortures him first:

The voices came close now. George raised the gun and listend to the voices.

Lennie begged, "Le's do it now. Le's get that place now."

"Sure Right now. I gotta. We gotta."

And George raised the gun and steadied it, and he brought the muzzle of it close to the back of Lennie's head. The hand shook violently, but his face set and his hand steadied. He pulled the trigger."

Other examples:

Lennie's last name is small.
Lennie is a big, strong, powerful worker who doesn't use his physicality to harm people (on purpose).
The same gun that put Candy's dog out of its suffering and misery does the same for Lennie.
Everyone on the ranch feels really badly for Candy when his dog is shot, but no one except Slim feels that way for George after losing his best friend.
George spends the novel complaining about having to take care of Lennie but doesn't feel the real pain until Lennie is dead.
There are other smaller examples, too.