Is there any way of ordering/sorting vectors?
If I understand your question correctly, you're looking for something that another (beyond KD-trees) standard space partitioning algorithm does. This one is called BSP-trees (for Binary Space Partition) and it uses vectors instead of dimensions for its space subdivision/partitioning. You can see it contrasted to KD-trees in slide 29 (previewed below) and beyond of this presentation.



The criterion that is used in the algorithm is intended to balance the data in the branches of the tree. This guides the definition of an order on vectors for what seems to be your purpose as well.

Otherwise, more generally speaking, one way to define a total order on a vector space is by identifying an order vector. Then your ordering is defined by the dot product with this vector. This represents projecting the entire space on the line defined by the vector and thus using the total order of the one-dimensional space it defines. For a more detailed explanation of the dot product, consider this video.