I think Oskar only wears white to continue to hide what'r really going on inside of him. On the inside he going through a rough ride of emotions at such a young age. However, he would prefer the people close to him to know nothing about it or that he really doesn't know how to handle the things happening in his life. White, a color characterized as pure and innocent, is a perfect disguise for his covered feelings.
I believe Oskar wears white to remind him to look optimistically at why his father died and also for remembrance.
I think that Oskar wears white so that people do not know how his mourns the loss of his father. Since black is the customary color for mourning, Oskar wears white to convince people that he is ok.
Also, white reflects all other colors. Perhaps he feels as though he has too much to think about so he wants everything to "bounce off of him". He doesn't want anyone to see who he really is, so he wears white to keep their gaze from penetrating him, perceiving his true grief. (This is all metaphorical/symbolic, not in the literal sense.)
But in some places white is the customary color for mourning.
This is characterization of Oskar