the Atheros ability is a triggered ability, not a replacement effect. If it were a replacement effect, the creature would never hit the graveyard (something like "If a permanent would be put into a graveyard from play, instead return it to your hand unless...").
It's an effect that triggers when something "dies," which is a term that means "is put into the graveyard."
"700.4. The term dies means “is put into a graveyard from the battlefield.”"
So yes, Myr would still trigger because the creature, no matter what happens, will go to your graveyard (unless you have something with an anti gy replacement effect like
Wheel of Sun and Moon or
Leyline of the Void). If they pay 3 life, the creature stays there.
If a haunt creature dies, you end up with 2 triggers, both controlled by you. Trigger 1 is "return to hand if opponent pays 3 life," and trigger 2 is "
exile haunting." You, as the controller of both triggers, would chose which order to put them on the stack, since they occur simultaneously affecting the same permanent. If you wanted the "haunt" trigger to happen, you'd put trigger 1 on the stack first, then trigger 2. Trigger 2 would resolve, which would
exile the creature, and trigger 1 would be moot. If you wanted the "opponent can pay 3 life" trigger to happen, you'd do the opposite.