I find it hard to know when to play jarraxus in control matchups. Against warrior i assume you want to play it sort of early to start pressuring with your 2 mana 6/6s?
This is something you need a ton of experience with and there's no easy answer to it. It's something I struggled with a lot early on.
In the Handlock vs Control Warrior match up it's this game of back and forth where the Handlock player presents threats and the CW tries to remove while also gaining tempo off of the removal (due to the 1 mana removals). Handlock tries to pressure the CW enough where the armor is as low as it can be by throwing the big minions.
With the Handlock hero power you gain card advantage and they start to run out of answers. HOWEVER... the more you tap, the more you put yourself into fatigue. If you don't tap then you would actually lose card advantage against CW as they can remove stuff more efficiently. If you don't tap and you Jaraxxus early then you might end up not having any cards in hand because you lose the Life Tap ability. If you Jaraxxus too late... the CW can wait until the fatigue damage brings you down to around 10-13 and then finish you with weapon plus Grommash hit.
The best time to pull out a Jaraxxus against CW is you have a couple of taunts up with DoA/Sunfury and they didn't Brawl the board AND you have a hand of like 8-9 cards with most of your answers in hand. You also want to use Jaraxxus after it has gotten an Emperor tick so that you can do Jaraxxus plus Hero power on the same turn. A good CW player knows this and will always try to make it difficult for you to Jaraxxus by always presenting a threat on board.
The next level stuff is if he has Grommash or not. That's why you need the taunted bodies up, you don't want to use Jaraxxus and then get killed by Grommash. This also requires experience but sometimes you can tell if they have Grommash or not. This is why saving heals until after Jaraxxus is also important because what may happen is that they might equip a Gorehowl or start hitting your face with their weapons.
The Cthun Warrior match up is even more intricate and for me more difficult. The deck plays more minions and you need to have more answers early on. Otherwise you might find yourself in a bad position and then killed by a big Cthun. In this match up I always save my Sylvanas and Shadowflame for the Cthun if possible because I don't want the Brann + Doomcaller going off after Cthun gets played. I generally have to play a lot more aggressive in this match up. The good Cthun Warrior player will save a Shield Slam for their own Cthun so I take into account with my count of their removals.
The Renolock match ups even less in favor of the Warlock because you simply have less powerful threats. Far fewer 8/8s, one less massive Twilight Drake. You have to rely harder on your Jaraxxus to win it for you or your Nzoth.
TLDR: Use Jaraxxus in the mid late game when you have big card advantage and a board with taunts that can protect you from Grommash burst. Against Cthun Warrior you need to have a solid board in play to absorb the Cthun hits and save a Sylvanas + Shadowflame to steal the Cthun (or Sylvanas + PO). In either match up you need to play the aggressor. Don't Jaraxxus too late when you are about to fatigue, you will not have enough burst damage to finish off a CW.
As far as other match ups go. Nzoth Paladin doesn't have a lot of burst so you can Jaraxxus when in a decent enough spot (ie. not facing down a massive board). You save Twisting Nether for their Nzoth turn. Same thing for Priest only you are even safer when it comes to Jaraxxus usage... the main thing to know here is that you want to hard mulligan for Jaraxxus if you know a slow Priest is coming (which is like 90% of Priest decks anyway). You don't want them Thoughstealing your Jaraxxus, that's one way to lose a very easy match up. Anyfin Paladin is a problem because they have big burst but it takes time for them to build up to it and you can pressure them before they are able to pull it off. The key against Paladin is to bait out the double Equalities and then build a massive board with Nzoth.