I think that Oskar invents things in order to protect others and himself. He often invents things that relate to buildings falling, like his invention of buildings moving up and down, not elevators/people. If buildings were on the ground level, his dad wouldn't've died. Also, the birdseed shirt symbolizes Oskars regret and blame for his father's death. Oskar continues to invent ways for people to not be in unsafe situations so that maybe they can avoid death and the feelings associated with it.
I agree with the ideas above, but I think that that inventing is also a coping mechanism for Oskar. Its a way to get his mind off his father and imagine how things could be. In addition to this, I think its something he feels he needs to do, and if he doesn't invent, he might just be overwhelmed by his own mind.
The significance of inventions can be connected with the bird motif. When a bird hits a window, it never sees it coming because it is confused. It is like being attacked by something that it unknown or unexpected which relates to the events of 9/11. Each bird that hits the windows of the twin tower symbolizes the unexpected, or something that can't be prepared for (a.k.a the planes). I think this is why Oskar wants to create inventions, as a need to feel safe and prepared for something that he feels like could be prevented in the future.
My personal opinion on why Oskar makes up all of these differnt inventions is that it is something he can express what he wants or wishs would happen in his life. For example his birdseed shirt is an invention of his becuase he would of wanted a birdseed shirt to have saved his dad from the 9/11 tragedy. Maybe his inventions let him deal with things that happen in his life in a differnt way than someone else would.
This of course relates to the Inventions page.
Link to Birds