Reading the informations about these items (Midnight Shards or Stone of Insight) I can tell that the experience will not be increased, once that the experience you gain is based on your level, not by killing monsters.
The same I can tell about tasks, the event exp increase the experience you gain by killing monsters, so other forms of earn experience will not be affected by the event.
This is the message when an event is active, it says only about killing monsters.
"Skill Event! Your skills improve at a faster rate.
XP Event! Killing monsters yields more XP.