How to Extract Nonorthogonal PCA Principal Components
Let's say x,y and z are your basis vectors and you mix them to get what you are calling your mixed sources. If your basis vectors were (x-y), y, and (z+y) then you could mix them in a different way and end up with the same mixed sources. 

Basically, there are many ways to come up with a set of basis vectors for your signals. You need to say what kind of basis you want. It is not enough to say that the basis vectors are non-orthogonal.