How to not keep saying "says X" or similar if dialog is between 3 or more characters yet still show who's speaking?

Use action tags instead.

"So I went to this Wicked party last night!" Sara exclaimed.

"Yeah?" Tony asked, not really interested.

"It was really fun." Sara looked down at her shoes sheepishly.

"I'm sure it was!" Jared assured her. "How much beer was there."

Sara looked at her friend oddly. "None. It was a Wicked party for underage kids"

"And no beer?" Jared obviously didn't believe her.

Tony rolled his eyes. "I don't see how it could have been that wicked, then."

Sara's eyes widened in realization "Wicked themed! People were dressed up like characters from Wicked, and we got to go to the broadway play!"

Using action tags makes it easy to follow a conversation as well as visualize what's going on between the characters.

First, use "said." Do not write fiction in the present tense.

Second, "X said" is a convention that is all but invisible to readers. Use it when it is necessary without hesitation.

Third, seldom have more than two or three speakers in a passage of dialogue. They should have characteristic ways of speaking so you do not have to attribute every speech.

Better say it too much than too little.