For the "Under the Shadow" quest you need to collect 10 Necrotic Runes. These runes are an uncommon item (though they are very common in drop rate) which you can get from killing any undead / scourge mob around a necropolis spawn point. You can find the zones these necropolises are in by looking for a purple skull on your continent map. Be forewarned though, there's a lot of people farming these items and you'll be hard pressed to get any without a group.
The "Shadows of Doom" quest requires you to kill an elite mob, a Shadow of Doom. These mobs don't hit very hard but are rather difficult to get a hold of unless you're in a group with a plan. In order to make a Shadow of Doom mob appear, you need to give 8 Necrotic Runes to a priest NPC near a necropolis spawn point – they're in the same area you'll pick up the Necrotic Runes from. To complete the Shadows of Doom quest, you'll only need to kill one Shadow of Doom.
Gallery: Argent Dawn Zombie Rewards