Greetings,
The problem is certainly interesting and seemingly simple. Unfortunately the solution is not equally simple. What hardware is used is secondary (Arduino/PI + Multiple Cameras) but the image processing part is the most important to get accurate results. One has to determine the 3D aspects of the objects in order to estimate the volume and that processing is involved.
I have relevant expertise with Arduino/PI, Cameras, Image Processing - please see my profile for details. However it doesn't seem doable in the budget you have. So if you are open for the budget I have bid, feel free to get in touch. We can discuss details and take it forward.
T & R
Alok Pugalia