The bird
The bird is a dual symbol in the novel, firstly because it appears as an auxiliary symbol in each part of the novel, but also because the story's flavor changes in each part, and the bird is listed in the title in a different way for all three parts. Therefore, the bird seems to represent a part of the human unconscious. Perhaps the bird represents Toru's soul, or perhaps as the title "Thieving Magpie," perhaps the bird represents the hidden power behind the novel's mystery, as if nature were randomly attacking Toru. (Magpies are famous for seasonally attacking humans en masse.)
Mr. Honda's departing gift
Toru is given a gift by Mr. Honda by way of last will and testament. The symbol seems to represent the lack of a father figure in the story, symbolized by Mr. Honda's unique position as the only older gentlemen in the plot, and the fact that what was inherited was literally a box of nothing. No doubt, this signifies the tone for the rest of the novel in which Toru loses his wife, his dignity, his future, all to what end?
The motif of missing people
First, the cat goes missing. Then Kumiko goes missing, and often, when Toru feels he needs someone to talk to, May is missing. This motif achieves a sense of lostness and confusion, as if Toru is detached from reality, trapped in a dream or something.
The sexy phone call
When a mysterious woman calls Toru, he answers and without warning, she brings herself to full orgasm over the phone. He feels disturbed and invaded. The meaning of this aggressive female sexuality seems to parallel the fact that in every moment of the novel, Toru is being tormented by his fascination with women who reject him. Perhaps the idea is something like, "Toru does attract women, but he can't seem to find the ones who want him." But nevertheless, the effect of the call effects Toru like an act of sexual harrassment, and a good argument can be made for that. The meaning of the call then would signify Toru as the object of female abuse (and a good argument can be made that Kumiko is abusive).
The false violence.
Several times in the novel, Toru thinks he violently attacked someone, but in reality the are merely an apparition, summoned by with wife. The image seems to represent a wife who keeps her husband's loyalty by making him defend her from suitors. The metaphor is complete in that Kumiko has literally cuckolded her husband by her sensual affairs.