In Chapters 15-17, what is an example of situational irony? What is an example of dramatic irony?

Situational irony is what most people think irony is in general. It is the incongruity with what is expected to happen and what actually does happen. This kind of irony is generally described as "the opposite of what you expect to happen does happen." It does not necessarily have to be the opposite. The result simply has to be unexpected. 

In Chapter 15, a group of men challenge Atticus at the jail in Maycomb. They...

Situational irony is what most people think irony is in general. It is the incongruity with what is expected to happen and what actually does happen. This kind of irony is generally described as "the opposite of what you expect to happen does happen." It does not necessarily have to be the opposite. The result simply has to be unexpected. 

In Chapter 15, a group of men challenge Atticus at the jail in Maycomb. They have come to get Tom Robinson and Atticus is there to talk them out of it. With the tension rising, Scout rushes over to the men and begins talking with Walter Cunningham Sr., a member of this mob. No one could have expected that Scout's awkward conversation (monologue, really) with Walter Sr. would convince him to make the mob clear out. But this is what happens. After a final awkward pause, Walter amiably responds to Scout's request to say hello to Walter Jr. for her: 

“I’ll tell him you said hey, little lady,” he said. Then he straightened up and waved a big paw. “Let’s clear out,” he called. “Let’s get going, boys.” 

Dramatic irony occurs when the spectator (or reader) knows something that a character does not. Thus, the reader is a step ahead of the character. This is quite clear in Chapter 17 when the reader (via Atticus's questioning) is given clues that Atticus is suggesting that Bob Ewell is more likely to have hit Mayella than Tom. Atticus gets Bob to agree with Tate's assessment of Mayella's injuries. Then he shows that Bob is left-handed and thus quite likely that Bob could have been Mayella's attacker. We, readers, have this information before Bob is aware of it. Scout considers this at the end of the chapter: 

Atticus was trying to show, it seemed to me, that Mr. Ewell could have beaten up Mayella. That much I could follow. If her right eye was blacked and she was beaten mostly on the right side of the face, it would tend to show that a left-handed person did it. 

In a later chapter, Atticus will reveal that Tom's left hand is essentially useless, placing even more suspicion on Bob Ewell.