I've not been able to figure this one out and there doesn't seem to be a rteset.

Diagonally, each square seems to be the mirror opposite. That isn't working for me tho.

You have to have one and only one of the 4 symbols in each row, colums and square
Something like:

1 2 | 3 4
3 4 | 1 2
--------------
2 3 | 4 1
4 1 | 2 3

MINOR PUZZLE SPOILER******

Look at the blocks that cannot move. You know the ones that do won't be those icons, because of the message from the mouth that the icons cannot match in rows or columns.

It's easiest to start with a row that only has one or two moveable blocks, and go from there.

I think it's pretty much a standard Sudoku riddle, just with symbols instead of numbers.