There are points, randomly scattered, to make a procedural order that they always were as follows:

0 1 2
3 4 5
6 7 8

Actually point may not have the correct topology can be stretched in different directions.
How can I change the order of the points? I tried to use the Sort SOP, but it is not much help. Does anyone have any ideas?

I don't think so you tried very long time Sort SOP.

Anyway, here the solution:
1. one Sort SOP, and sort points ‘by x’
2. another one, and sort points ‘by z’

Voilà

Thank you, fsimerey! Yes, the methods of double sorting everything works.
But this will not work if the points will be some movement on its axis relative to each other.

It's hard to know what you want to do, but here's an line of thought: you can create lots of additional point attributes attached to each point with an ATTRIBUTE CREATE SOP. This might lead you down the right track for what you want to do.

For example, to start, you could make a new point attribute called ‘origPt’ and copy the point number values to this new attribute. Now you have the point numbers, and the original point numbers. If you do a sort, the point numbers will change, but the ‘origPt’ attributes do not. They stay unchanged.

Now, you could have attributes which represent the “point numbers” for sorting along each axis. The Sort Sop will only change the ‘built-in’ point numbers attribute, but there's many SOPS which address user-added attributes. Hit Tab in SOP's Network and look in the Attributes Menu. Add as many new point attributes as you like, for a view along each axis, etc.. HTH. b.