Azrael is generally the point character for most his teams due to his incredible value with one bar. If you get a hit, you can get over 9k damage, take them to the corner, and set up for 2A(A) oki that can potentially kill their point character. The route mentioned is also burst safe and can cause the same situation to the opposing teams burst depending on said team. Azrael also generally needs a assist to be very effective due to a lack of solo mix options. This means having him first with an assist and burst potential at the ready is a good thing. He also is very good at generating meter due to his damage.
There are a few teams that want Az on the back line. Most of these comps have partners that have very strong round start options (Mitsu 5A, Carmine 5A, Aki ToD set up etc.) You generally want to make use of his strong 5P and force blockstun with his 6P. 4P is very strong as a anti-zoning tool so it can help with characters that don't enjoy getting shot. 4P can also be used as a bait to entice the opponent into punishing the assist only to punish them for extending.
S tier partners - Gordeau, Merkava, Vatista, Ruby, Narukami, and Akihiko
A tier partners - Carmine, Waldstein, Jubei, Hyde, Blake, and Ragna
Just because your favorite character isn't here doesn't mean you can't play the team. However for competition oriented players, these are your go to teams.
Here are quick thoughts on each S tier team.
Gordeau - Az/Gord is a solid team due to how well Azrael synergies with Gordeau's assists. Gustav+6P is very solid as a means to cover grounded approach and force + frames. It is also a good option to close in with and make dashing in neutral all the more threatening. 5P is a good lockdown tool and has fast enough start up to be threatening as well as slow enough too consistently get past cross up protection. 4P is fantastic with backdash and is a very good way to take a turn back. You can even active switch into Gord from this and get a combo. Outside of assists they have lots of CC damage and ways to open players up. Neo Guranzon is a very strong player who is currently playing this team, please refer to his match footage to see the team in action.
Merkava - Merkava has a lot of similarities to Gord however 5P is much faster. This can be a problem at times since it will get blocked due to cross up protection at longer ranges. Azrael also does a good job against some of Merkava's biggest problems like Nu. There are currently no notable players running this team but it is highly advised.
Vatista - Her assists are very very good for Azrael. Her 4P contests air space where Azrael has a hard time reaching safely. 5P is a good lockdown tool and incredibly easy to hit confirm from. Strong neutral from her 6P and works similar to Gordeau's 6P. She also has synergy from instant j.C+6P for lots of damage. There are currently no notable players running this team.
Ruby - Ruby has good assists for Azrael and lots of active switch potential. Her assists work similar to Gord however her 4P is better and 6P is much faster overall so it allows for a faster paced team. Ruby's mobility and ability to play without assists is fantastic and allows Azrael to have ample time to heal. They also can get a lot of damage from instant j.C 214A+6P and have good ways to turn small hits into huge damage. There are currently no notable players running this team.
Narukami - Yu has a lot of tools that Azrael likes and functions similar to Ruby in a lot of aspects. 6P is fantastic for neutral and can even led to conversions from Gustav+6P at a given space. 5P is similar to Gord's and 4P is similar to Ruby as well. The team also gets big damage from j.C 214A+6P. Currently C50P plays this team.
Akihiko - Aki/Az is explosive damage and due to the changes, Aki doesn't fall into a lot of brawler struggles anymore. Neither really gain anything from their assists in neutral however in combo they lead to massive damage and can be used in combo to set up sandwich situations. Currently Sethlolol plays this team.
Azrael has a lot riding on dash assist and Gustav. You want to use dash to create sandwiches very easily and go for CC mix up a lot to get your openings. Azrael has a execution barrier in his just frames however you can mash many of these fairly consistently. As the Azrael player, you want to make sure you're managing your assists health as a solo game is very hard for Azrael in many MUs. Your assist is your mix so a picked of character can lead to a lot of struggle opening a competent opponent up.
Generally 2A(A)/2C(C) in corner is his best oki to cover all tech options and create safe cross up assist on wake up. DP and TCL are both common and strong enders as well. This video explains a lot of these options. https://youtu.be/rqzcYpZWn3E?t=267 2A(A) is now consistent from Valiant as well.
Azrael does not have much in airtight strings. Most of the time he relies on special canceling into Gustav or 5AAA can be air tight in many situations. 5B>Gustav is also a block string depending on spacing and when you cancel into Gustav. He relies more on stagger pressure and ending strings early once the opponent is encouraged to DP. Once they DP, they die pretty much die lmao.
Tips and Tricks
You can special cancel the jump start up of Azrael's forward dash thus letting you have more options to approach with. These are refereed to as TKs despite not necessarily being correct. This mainly due to them being the same input. You can also cross up with his dash and TK a special to get left/right mix. Most of these are reactable and not very rewarding without assist however they are good to deal that last bit of damage needed to win a match. You can also special cancel the landing frames of Azrael's j.C for more pressure or even combos.
Azrael struggles in neutral, so force as many neutral situations as possible. Many pokes deal with Azrael very well and playing outside of his 5B range or in the space where 5A whiffs is very good. Stop commiting in neutral because you will die against for going in too hard. Play it slow, create as space as possible, and let them hang themselves in neutral.
If you are a zoner, stop throwing projectiles without a second thought. Set yourself up to be out of phalanx's path or place yourself in a position where you can punish them for going for bad growlers. Patience is key to beating Azrael consistently.