Can you use Map of Earnil on cards like A Test of Will or Hasty Stroke to trigger their responses?

Since Map of Earnil uses an action to play the event card, I wouldn't think so.

I also think you can't. You will have to choose a dwarf tomb to bring the event in hand. And you need to do this before knowing if it where an annoying effect.

I can confirm what dalestephenson and Rouxxor have said - since Map of Earnil is an Action, you need an action window to use it, and so it doesn't work for events which are Responses (Map of Earnil on Dwarven Tomb to return AToW to your hand is legit though).

Obviously this applies equally to the Record attachments in the other three spheres and any Response events there.