Finding diagonal objects of an object in 3d space

One solution would be to get the normal vector between the objects and look at its x and z components. Diagonal objects will have an identical x and z length (assuming the objects are arranged on the X/Z plane, otherwise you'd have to swap components accordingly).

In code:

// MyObjects is an array or list of your corner GameObjects (1-8)
// K is your center GameObject
foreach(GameObject obj in MyObjects){
    Vector3 normal = (obj.transform.position - K.transform.position).normalized;
    // compare against a small float because of floating-point inaccuracies
    if(Mathf.Abs(Mathf.Abs(normal.x) - Mathf.Abs(normal.z)) < 0.001){
        // diagonal object detected!
    }
}

If (distance between 4 & K) == (distance between K & 3) = (distance between 2 & K) than it's a circle, therefore there's no diagonal :) If there was a diagonal the distance between the diagonal would be sqrt(2) times bigger than the distance between the adjacent.

Pick one of the objects that is not K, and order the others by distance (ignore K). Exclude the object you picked, 4th, 5th and the last one.

Example, if you picked 1, ordering the others by distance from one would result:

2, 4

3, 6

5, 7

8

You'd remove 1 (the one you picked), 3 and 6 (4th, 5th), 8 (the last).