What are the exact meanings of roll, pitch and yaw?
The key thing missing in your interpretation is that the order is important. Applying the same roll, pitch and yaw angles in a different order will result in a different orientation (mathematically this is because rotation matrices do not commute).

The correct order is:


Yaw (for an airplane this is typically called the heading)
Pitch
Roll


For any given attitude, there is a unique combination of yaw, pitch and roll angles that will (if applied in this order) give you the correct attitude. 

These angles are only meaningful in a given coordinate system. We typically use a system where all angles zero means you are pointing North and wings and body are parallel to the ground. Based on this starting point you would apply the given angles.


(source: Wikimedia from this Wikipedia article: Aircraft principal axes)

See also the answer to this question:
What is the relation between roll angle and pitch angle?



Let me expand a bit on your example:

We start will all angles equal to zero (level, pointing North) and pitch up 90 degrees such that our nose points straight into the sky. Yaw and roll have not changed. Now we start rolling. The roll angle would now tell us in which direction the belly of the aircraft is pointing (0 degrees means belly pointing North, 90 degrees means belly pointing West and right wing pointing North, and so on).