Oberon will be a week or so after Koyanskaya (Part 3 releases on the 10th, we should get Anniversary early next month before it). Between the two, Oberon is going to be the harder one to get. If you don't pay for GSSR banners, he won't return for 18 months. Koyanskaya is back next New Years event.

Get Oberon now since Koyans will back at Next year, at January 2024. You can try to get them both. As for Arjuna Alter, you can do it, but imo it's better to focus it with your Morgan since they works relatively the same.

You don't NEED Oberon for anything. He's very strong but is a luxury. Not a necessity if you have koyanskaya. Definitely go for you favorites. For buster you need either koyanskaya or Oberon. Not both. Of course you can do the highest possible damage if you have both, but as long as you have at least one other 50% charger you can borrow the one you don't have, or use double koyan plus said 50% charger for almost anything.

Strongly disagree with the comment above. Oberon is absolutely necessary for 3T on 90++ nodes. Whether that's important to you or not is a separate matter.

As for your questions:

So is Oberon necessary getting now? Or can I wait a year and everything still be ok?

Depends. If you want to 3T 90++ nodes, it's necessary to get him now. If not, you can simply ignore him. There is a reason to skip him now though. Since you said you want the Trung Sisters, Koyanskaya's second rate-up will be very inconvenient to roll on, as she returns right before the sisters' debut.

Should I try to Anniversary summon for Arjuna Alter?

He is somewhat similar to Morgan. Sure, he deals more damage, but he has way less survivability than her. Also, although he doesn't strictly need Oberon to farm, his damage only goes nuts with the moth man. I think you should skip him.

Going for targets because of gameplay reason only is probably not the best choice. Go for who you are very much sure you'll make great use of. Not a single character in the game is necessary, there are many roads leading to Rome. It's more a matter if the characters you want fit in for your personal game play.