Who is this referring to? "of the sixteen rooms in his home in kenilworth, illinois, his favorite was the seventeenth, the oom room"
It has been years since I read the book or saw the movie but there is some reference in the olden days around the 1800s of an extra room that was considered to be hidden away that was referred to as the Disappointment room or the oom room. The room was used to house children that were considered to be mentally ill or handicapped in some way (before the word disability was used).
The boy in the story already feels like a derelict in his home so this could be the reason that he uses this expression. I could see very well how he would have been intelligent enough to have come up with the idea of the oom room.