You should keep Fire Plume's Heart in most match-ups, except for aggro.
Reckless Flurry can be an amazing turn 3 clear vs aggro paladin and druid decks, as well as a later-turn clear.
Stonehill Defender and Tar Creeper are powerful turn 3 cards and helpful in completing the quest.
I know it’s really early and most of Witchwood cards haven’t been revealed yet, but this is a good place to start. Once better odd-cost cards have been revealed, you will be able to potentially use them instead of: whirlwind, acolyte of pain, frothing berserker, Zola the Gorgon, Baron Geddon, tar lord. I think the rest of the deck is a pretty good baseline for Odd Quest Warrior. Suggestions are welcome.