How to delay a loop in android without using thread.sleep?

You can use a Handler instead of for loop. You should not call Thread.sleep() on the UI thread.

final Handler handler = new Handler();
Runnable runnable = new Runnable() { 
    @Override
    public void run() {
        // do something
        handler.postDelayed(this, 1000L);  // 1 second delay
    }
};
handler.post(runnable);

The following code doing the task in every second:

final Handler handler = new Handler();
Runnable task = new Runnable() {
    @Override
    public void run() {
        Log.d(TAG, "Doing task");
        handler.postDelayed(this, 1000);
    }
};
handler.post(task); 

Your for loop should be:

final ImageButton[] all= {btn1, btn2, btn3, btn4};
Handler handler1 = new Handler();
for (int a = 1; a<=all.length ;a++) {
    handler1.postDelayed(new Runnable() {

         @Override
         public void run() {
              ImageButton btn5 = all[random.nextInt(all.length)];
              btn5.setBackgroundColor(Color.RED);
         }
         }, 1000 * a);
    } 
}

This way it achieves your desired behavior of staggering the color change.

Edited for syntax