Certainly makes for a thematic choice should you draw your clerical powers from the stygian force that patrons your proud household. Before you go that route (and I encourage you do) might I suggest that, rather than a domain we've seen time and time again like evil or war etc., you play off the lawful nature of the setting itself? Since one's faith will greatly influence their personal quirks you've a wonderful chance to seek out certain quirks to adhere to beyond those usually associated with secular life. For example:

Maybe the demonic god you worship is considered the anti-saint of a certain virtue--while not being outright evil you could get a lot of mileage out of conducting yourself in a manner your covenant demands. Likewise you could place something petty, mundane or surreal as one of the powerful beings chief concerns and--as it only has agency on the mortal plane through you--be expected to act accordingly. Such as:

*Iconoclasm - You're expected to destroy the items, icon and monuments to other religions when it's within your power to do so
*Stipulations - You must always impose an additional requirement to any deal or proposal proffered to you
*Technophobia - Stymie the advance, abstain from the use of and otherwise be hostile towards sufficiently complex machines.
*Commerce - Heal the party sure, but demand a tithe towards your deity to do so. No matter how dire.
*alliteration - Your deity demands a definite display of deft diatribe. Subsequent syllables should be stressed when speaking.
*Limerick - Must preface the use of clerical spells with a jaunty rhyme.
ETC

Keeping in the spirit of this you could conceive of some bizarre ritual to cover the blanket term of 'communing' with your deity.

Heck, if you decide to go the whole God of the Wastes route you could even just be voluntold to become a cleric by some force you stumble upon in our adventures (since you won't start with it), having a mutually beneficial yet antagonistic relationship with your deity.

Regardless I hope to be an engaging accessory to your adventures via my atypical 'barbarian'