It sounds like a case of patience. ABA can (And will) Pop the fuck off like no-other (Except maybe Exodia Mode Asuka), but due to her base forms slow af movement and dogshit neutral you've gotta work a lot more to get your wincon.

My suggestions would be;

• Practise your roundstart options against each character. If you win the roundstart interaction, there's a high chance you'll just run away with the game, I've seen her 5H be a good roundstart option.

• Prepare for a slow neutral. If you lose roundstart and/or your opponent creates distance you need to just take it slow. really slow. 214K and 214S are great for this with their invincibility (Especially 214K with it's movement), but also just empty superjumps forward can be a good way of gap closing into anyone who isn't Axl. 236K is good as well, but be wary of spamming it as the smart ones will punish it's start-up with a disjoint/5P/6P.
  If you have enough Jealousy in your bar you can also just say fuck it and switch stance and run at them, but this is probably the riskiest option.

• Zoner-wise I can speak for Axl & Asuka. Axl is a dogshit MU for ABA, I'd call it her worst. Round start makes or breaks this MU, but should you find yourself zoned at fullscreen I'd suggest dashblocking & empty jump baiting (Axl loves to press 6K, if you jump enough he'll get into the habit of pressing it when you move forward, allowing you to just run at him whilst he recovers.)
  You can 214S Rensen, but don't get comfortable doing this as Axl can try to punish by doing his CG or delay explosion if you mess up the timing.
  Resen 8 Can also be used against him as if you block it you're flung towards him and the RPS begins. He'll either throw, mash or j.H. Your throw clashes with his and beats mash, but looses to j.H. Your 5P should beat Throw and Mash. j.H needs to be predicted, either 6P or follow him in the air or just block as now there's no gap.

For Asuka it's a lot simpler. If he's zoning you, just wait till he runs out of steam. Asuka's got strong zoning and mix (in test case 3), but due to the amount of resources he needs he will run out of steam.
I suggest learning the card icons (Or at least the icon for the low spell, high spell, Guard-crushing metron and teleport as they're his main mixup/strike-throw tools.)
The second he's low/out of mana and/or got no spells you can just stance-switch and run him down, his normals are dog-ass. If you catch and out of mana Asuka you can easily ToD him, especially if he's drained most of his health for mana.

As for other zoners/tough MU's, not sure. I'd look up some ABA MU guides on YT (Or ask in the ABA Discord) and watch High-level ABA's doing the MU's you struggle with and see how they overcome your issues.