It will not trigger on itself going to the graveyard, or on any other cards going to the graveyard at the same time. This means that neither itself nor other cards put into the graveyard at the same time as it will get exiled.

If spell is used to destroy Planar Void, it goes to the graveyard, then the spell goes to the graveyard. The spell is not exiled, as Planar Void was not on the battlefield when it was put into the graveyard.

The card does go to the graveyard before it is exiled, so other triggered abilities will trigger on the card going to the graveyard.