Rain down upon them!
Jaraxxus' basic attacks reduce the cooldown of Inferno! by 1, and increases its duration by 0.25. Every 3rd Basic Attack doubles this bonus.
Feast, my Minions!
Quest: Hellhounds now deal 3 mana damage per attack.
Quest: After hellhounds deal a total of 100 mana damage, they are immune to Spell Damage permanetly.
Crush them, minions!
Quest: Felguard deal additional damage equal to 1% of their target's Maximum Health.
Reward: After Felguard deal a total of 5,000 damage against heroes, Felguard gain 25 Physical Armor and taunt the closest hero within Demonic Squadron's cast range for 1.5 seconds.
Burn them down!
Quest: Fel Imps deal 100% additional damage against Stunned enemies. Felspire stuns enemies for 1 second after being pushed away by Felspire.
Reward: After Felspire has stunned every unique hero on the enemy team, Felspire also spawns Fel Imps for 10 seconds.
First I would replace Chaotic Energy with Surge of Power as his trait. Make surge of Power keep its mana cost of 100, but let it be triggered when ever, at the cost of doubling the cooldown of the ability. Give surge of power a 30-40 second cooldown as well.
His basic abilities are fine as is, and are really cool, as are his ultimates. However, I would make Chaos bolt set the cooldown of surge of power to 0 when it kills an enemy instead of a random basic ability. Random effects aren't very fun in mobas, but the kit you got for jaraxxus here has potential to be good.
Now for the talents..
Oblivion is a cool concept, however it needs its power tuned back a little, or moved to level 20. In particular the bonus to Incinerate flesh is WAY too strong.
I LOVE you face jaraxxus. It practically lets you label this as a muti-class concept since it flat out turns him into a warrior. Really well done talent. I gotta say, same applies to the other concept, you have really cool talent ideas in general.
All of his tier 2 talents are great, even if 'vanished to the nether' might be a bit on the weaker side. Maybe buff it to 3 seconds?
For tier 3, I think shadow Flame needs a bit of a nerf. Make it only disable the channeled ability for 6 seconds, without the silence. Otherwise, great talent ideas yet again.
Tier 5, mage hunter and warrior hunter need their armor boosts reduced to 15 I would say, and no armor what so ever on Titan Hunter.
Tier 6: Shadow fury needs its damage toned back a tiny bit, thats a LOT of damaged tied to a silence, even if its on a long cooldown. Either increase the cooldown to 40 seconds(and make the quest reduce it to 30), or tone back the damage a little.
Tier 7, Rain of chaos is a really cool talent. However the random ability to hurt your team is a bit ridicious. Perhaps make it so he flies up and charges a chaos bolt that does 50% more damage, and while hes channeling it he rains down the smaller Chaos bolts in the area below him. Keep the same negative downsides though.
Soul Corruption is fine as is.
Either keep surge of power how it is(with a different name and without 'allowing you to cast' surge of power as thats now his trait), or replace it with OBLIVION.
These are just suggestions though. I hope you come back and work on this more because this has potential to be really cool.