Neutral Special - Gohadouken/Zanku Hadouken
Akuma's Hadouken, when Akuma use the neutral special in the air it becomes Zanku Hadouken, it's basically the same Hadouken but unlike Ryu and Ken he shoots his fireball diagonal downwards. Use the QCF + Attack input to enhance the attack becoming multi hit and in the case of Zanku Hadouken launching two (slight smaller) fireballs at the same time. When Akuma is under the effects of the Satsui no Hado he will always do the enhanced version of the attack,
Side Special - Tatsumaki Zankukyaku
Akuma's Tatsumaki is different of both Ryu and Ken since it's stronger than Ryu but its affected by gravity meaning that it doesn't work has a horizontal recovery. Use the QCB + Attack input to do a stronger version of the move.
Up Special - Goshoryuken
Akuma's Shoryuken, it's similar to Ryu's one but it has more power, do the S + Attack input to do an enhanced version that adds a second hit to the attack, when Akuma is under the effects of the Satsui no Hado you can press the button again and do a follow up where Akuma gabs his opponent slaming them to the ground.
Down Special - Hyakkishu
Hyakkishu (or "the Demon Flip" for the ones that prefer named it in that way) is a command jump, if you don't know what that words mean basically is a regular jump made with a command but that it usually has some class of function that made it different of the regular jump, in Akuma's case he can do different attacks after jumping has follow-ups:
Note that much like Ryu and Ken's Down Special, this attack doesn't has an input version (but it's still affected by the light/medium/heavy mechanic)
Command Special - Sekia Goshoha
Much like Ryu he can also do a Shakunetsu Hadouken (even if his version is called Sekia Goshoha), unlike Ryu he can charge the move to make the fireball stronger, you can't use Sekia Goshoha in the air.
Final Smash - Kongou Kokuretsuzan/Misogi/Shun Goku Satsu
Akuma has three Final Smashes, two of them depends of the distance meanwhile the third one is a secret input-only, if you are near an opponent in the floor Akuma use Kongou Kokuretsuzan, Akuma charges energy in his hand and strikes the ground creating a wave of energy, if you are either far the opponent or in the air he uses Misogi, Akuma jumps offscreen and reappers quickly above the opponent (or the nearest one in the case that there are more than one) attacking with a devastating knifehand strike, if the opponent is above a pit he will only teleport to the border of the stage. If you input Jab, Jab, Forward Tilt + B meanwhile you are under the effects of the Smash Ball/SF Meter Akuma uses his ultimate technique the
Shun Goku Satsu, Akuma grabs an opponent and fades the screen to back as the target is relentlessly beaten showcased by a series of flashes. If Akuma is under the Satsui no Hado effect the move is cinematic showing a mix of the SFIV/Tekken 7 and SFV versions of the move, in any of the versions if after the move the opponent has 100% of damage or more it's instant killed, Akuma will pose at the end of the move (and has a side note, it will also be his victory pose if he finish the fight with this move).
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Has an additional note, Ashura Senku is his dodge, meaning that he actually has a special dodge, when Akuma is in Satsui no Hado mode he will also be able to use Ashura Zenku midair replacing his air dodge.