Each Alignment has two gods. Players who meet the requirements to choose a Devotion will be able to chose to devote themselves to either one of the Alignment's gods.
With The Order, you can choose to devote yourself to either Odin the Allfather, or Thor the Warrior. Odin is magic based, whereas Thor is physical.
As for The Chaos, on the other hand, you choose to devote yourself to either Hel the Infernal, or Loki the Mischievous. Likewise, Hel being magic based, Loki being physical.
After picking your Devotion, you will have access to make the respective god sets. But as for now, after picking your Devotion, for every kill in WoE, you will have a small chance, should your god likes you, to get a free legendary god item. So please remember to leave some room in your inventory because this doesn't come with a warning (simply can't).
Q) Do I need cursed kills to activate it?
No, you do not. The only requirements are to have joined an Alignment, reached PvP Level 30, and kill during WoE for your alignment's messenger to approach you.
Q) Must I be in the Devotion battle mode for a chance to obtain set parts?
No, it can be in any battle mode. However, the set parts will only take effect when you're in your Devotion battle mode.