The replaced phone/answering machine: Oskar is the only one who has heard the messages left by his father on the day of the 9-11 attacks. He quickly replaces the phone with an identical one so he prevent his mother from hearing the messages but also save them. This alone has tons of symbolic meaning - he's hiding something tragic (as he hides many things); he's holding on to something tragic - something that hurts him - but protects others from it, he is unable to let go and he realizes at the same time it is something harmful.
The missing lock to his father's key: tragic connection back to his father - symbolic of whatever is missing internally now that his father is gone; symbolic of the locked state of Oskar's heart and mind; this is the starting point of Oskar's journey - symbolic in itself.
The letters he writes to famous scientists: he's writing to ask for a job - he receives many form rejections which could be symbolic of another rejection he feels; he receives some with praise for his smartness - could be symbolic of the patrionization he often feels as well as the affirmation he desires
Besides those themes mentioned (which are major) I would like to come in with some hidden themes.
Did you consider the name Oscar and his family name Schell?
Try to analyse both from a phonetical point of view.
You could also take a look at the connection between Steven Hawking, his FULL book title and the physical way Mr. Black describes the pecularities of his bed.