I am looking for some clarification on wielding both relics and items. I've seen/played in both situations:
Can you wield a relic and an item with the same requirement?
For example: Can Bloodhawk wield Book of Lightning and Scroll of the Grave?

I'm pretty sure you can't, despite the rules being a bit vague:
"A warrior can wield multiple items, with the following restrictions:

-A warrior cannot wield more than one relic.

-No more than one item with the same requirement can be wielded by the same warrior.
-A relic cannot appear in one player’s army more than once.

-A warrior must have one item slot for every item it wishes to wield."

Also, a follow-up question: If you are unable to wield both, what if a relic has two requirements, such as Book of Souls(starburst+wand), would you be unable to wield an item of either requirement?

Relics are items, just items with a few more restrictions. So if an item and a Relic have the same requirement, you can't wield them both.

If a relic has multiple requirements, it counts against wielding another item for BOTH requirements. This also includes Faction requirements.