Ah, you should read this book. It's a lot of fun.
As far as conflicts, there are several conflicts. Actually, the book is made up of conflicts.
The two teenagers who are the main characters are in ongoing conflict with their parents. John is a kind of rebel, while Lorraine's mother is demanding and over-protective. John and Lorraine clash over a lot of things, such as how to treat Mr. Pignati. John and Lorraine are continually clashing with a number of kids at their high school, most often Norton Kelly. In a way, Mr. Pignati (the Pigman) is in conflict too, with reality. He denies his wife is dead, and then he fights to stay alive. That's just the main conflicts; there are more.