How calls Saeki: Just "Saeki"

Syusuke is his childhood rival an both were closest friends before they went to Junior School.

Normally, Saeki and Syusuke are paired in doubles games:
American Invitational Tournament Camp (only in the anime): they were in Sakaki's group and played doubles against Yanagi and Inui.
Beach Volley Tournament (only in the manga): When Rokkaku invited Seigaku to join to a special training, they made a mini beach-volley tournament. Saeki & Fuji were partners, wining all the games with their combined skills. But unfortunately, they lost against the old pair (Ryusaki-sensei & Ojii), so they had to drink Inui's new juice (have to mantion here that Fuji and Saeki didn't survived to it) and be the Silver seats for the winners (total humiliation).

How calls Saeki: Saeki-san

Saeki was closest to Syusuke, so he knows Yuuta too since they were children.

Like all the tennis club members, Saeki appreciates very much Ojii. He knows all them since they were children and learned tennis because of him.

During the match against Higa Chuu in the Nationals, Ojii 

How calls Saeki: Sae-san

Althought Kentarou is the captain of the team, Saeki is still his senpai and friend.  

How calls Saeki: Sae-chan ("-chan" is given to someone with your same age or younger than you, also used between closest people)

Like with all the Rokkaku guys, Itsuki is a closest friend of Saeki. They call each other "It-chan" and "Sae-chan" (obvious who belongs each nickname).

Amane Hikaru "David"

Althought Saeki can't understand David's puns, he's very pacient with him (unlike Bane, who hits him with a new lame pun xD)

In the Rikkaidai arc, Saeki says a pun before David could plan it.

Kurobane Harukaze "Bane"

The two of them get along very well. Sometimes, Saeki has to stop Bane when he wants to hit David (watch the short special Atobe kara no Okumono).

Ryou doesn't talk much in all the story, but we know that all the Rokkaku members get along very well since they were all children. Believe me or not, I found some Saeki/Ryou Fanfiction...

Not directly. Both teams have the best relationship than other schools (after Rokkaku, Seigaku have good terms with Fudoumine too). The two teams trained together before the Nationals (just in the manga) and they support each others in the matches.

In the Nationals, when Saeki is having his match against Higa's Kai and Rokkaku boys had to take Ojii to the ambulance, Seigau boys were there to support Saeki against Higa's cheer squad. 

Maybe you're asking "Why you mention Atsushi? They don't talk to each other in all the series". That's right, they don't even see the other's face in all the manga & anime, but remember that Atsuhi was in Rokkaku before Mizuki took him to St. Rudolph, so we suppose that both were good teammates in their childhood.