Kyoka has an excellent relationship with her parents. It was they who taught her music and thanks to them, Kyoka has found her way around a couple of instruments.
When she was young, Kyoka felt pressured into wanting to be a hero since her parents desire for her to become a musician, feeling guilty when she finally revealed this to them, but Kyotoku and Mika actually were surprisingly very understanding and received this welcomingly, supporting Kyoka’s dream that even continues to this day after the incident where Kyoka was poisoned by Mustard's knockout gas during the Vanguard Action Squad Invasion event. 
They seem to be good friends and are often seen together. The two heroes-in-training are paired together during the Battle Trial, and the Unforeseen Simulation Joint, showing to working well together. Kyoka is very helpful to Denki at the USJ, helping him to have more self-confidence about using his Quirk. As Denki thinks that he can't use his Quirk with Kyoka and Momo around, he is not able to use it well, but when forced to by Kyoka, he finally realized that he too can fight and be helpful. 
Kyoka happens to enjoy Denki's brainless state, finding it uncontrollably funny. Despite that, Denki does refer to Kyoka as a friend and she seems to view him in the same light as she hesitated to let a villain kill him. When Denki finds out about her insecurities around her music hobby, he compliments her, encouraging her to embrace her hobbies publicly, Kyoka gets flustered by his praise but is eventually convinced to pursue her hobby. 
During the raid on the Gunga Mountain Villa, Denki was panicking and fearing for his life, he thought about Kyoka when Midnight told him to think about the person who matters the most to him. It was implied that she knows of his feelings, as she had her earphones on the earth during the initial stages of the assault and replied to him after Denki looked at her. 
Momo and Kyoka appear to be close friends with each other. Along with Denki, the two battle against the Villain Alliance at the USJ, proving that they work well together. After that, they are often seen interacting with each other.
Kyoka later asks Momo to tutor her for the end of term test, which she accepted. 
When the class splits up to go shopping for the training camp, they pair up and go off shopping together. As well as this, Kyoka is proven to be somewhat defensive of her. During the summer training camp, she punches Hanta Sero for comparing Momo’s Quirk ability to convert fat at an atomic level into many different objects, to pooping. 
She later joins Kyoka's band, playing the keyboard, during the school School Festival and they pull off a wonderful performance with the teamwork of all of Class 1-A.
They are good terms as they are often seen talking as seen in Vs. Hero Killer Arc talking about their internships.
Kyoka is partnered with Koji during the Final Exams Arc against Present Mic. Although Koji is very shy and terrified of insects, Kyoka's words and example of bravery convince him to use his Quirk to talk to bugs of the forest, while she is annoyed that he picked that late of a moment to talk and help. Nevertheless, Koji later carries an injured Kyoka through the forest to cross the escape gate, and together they pass the exam. 
During the festival, Koji encourages Kyoka to play giving her more confidence.
They appear to good friends as they are often seen talking. During the Sports Festival, she is put off by Toru's desire to act as a cheerleader after they’re tricked by Denki and Minoru Mineta. She is also partnered up with Toru in the 'Test of Courage' during the Quirk Training Camp.
Toru is also thankful for Kyoka halting Minoru's attempted peeping in the locker room.
Despite not having too much interaction with each other, they mutually respect each other.
In Vs. Hero Killer Arc, Kyoka initially wonders how Izuku will do in the Rescue Training Race and is amazed by Izuku overcoming the drawbacks of his Quirk. Kyoka also finds Izuku's notebook very interesting and impressive, where Izuku notes his classmates' abilities.
During the School Festival Arc, a flashback of Kyoka and Izuku is shown. Kyoka asks Izuku for help on taking notes and they share a friendly moment with each other. They seem to be on friendly terms in the more recent chapters. During his struggles with Blackwhip, Kyoka is shown to be visibly worried for him. 
Katsuki and Kyoka's interactions at the start of the series have been minimal. They were first seen sitting next to each other on the bus when Jiro looks annoyed and freaked out by Katsuki's loud angry outbursts at Denki.
Starting from the School Festival Arc is when these two begin to develop a friendship. Kyoka asks Katsuki to help her in the Festival by playing guitar, he berates her and tells her he has no time for that. They are then seen working together and preparing for their performance with Katsuki listening to Kyoka instead of yelling as he usually would.
They are later paired up on the same team during the Class 1-A vs Class 1-B trials. Kyoka and Katsuki come to understand each other and put trust into one another. Katsuki, who always works solo, begins to trust his allies and relies on Kyoka as opposed to how he was when they worked together on their performance. Kyoka has shown to tolerate Katsuki’s personality more. Katsuki later comes to her aid when she was cornered by the opposing team in the Joint Training Battle. She is grateful and they went on to overpower their foes, achieving victory.