Run and Lala have been more or less friends since childhood. But unlike Ren, who loved Lala despite being treated similarly, Run holds a grudge against Lala for all the torment she made her go through, and spent several chapters trying to get revenge on Lala through various outrageous schemes and pranks, such as using the youth skunk and the clothes-destroying bomb. All of her attempts for revenge fail, and Lala is completely clueless of Run's feelings or her attempts at getting revenge. There are times when Run has a more friendly (or at least a more civil) relationship Lala.
Run considers herself to be Lala's rival in love, as she is also in love with Rito.
All of her childish and outrageous schemes to humiliate, harass, or get back at Lala end in failure, but overtime, her attempts become less frequent, perhaps due to skipping school often to work as an idol. She has since become more level-headed and mature.
Ren is Run's male counterpart (and technically, they are twins), who's shared the same body with her since birth, until they reached "adulthood", and the two to permanently split bodies. Run hates Lala but Ren is deeply in love with her. It was through Ren that she experienced the kiss he accidentally had with Rito, the cause of her love for Rito. Run hates it when Ren picks a fight with Rito over Lala, even calling him pitiful.
It was seen that Ren and Run are capable of communicating with each other while sharing a single body. They generally took turns with who lived in the shared body, while the other slept. Run eventually became the more prominent personality, and she would sometimes turn back into Ren in situations that are very undesirable for him, sometimes intentionally when the situation is undesirable for her.
After they became separate people, they began living together. It's not known in detail what their lives are like together, or how they get along. Ren has shown a slight care for Run, like when he advices Rito to not hurt her or any other girl.
Run has been in love with Rito since Rito and "Ren" accidentally kissed each other. Since then, she has tried her best to win him over Lala and make her look bad in front of him, although many of her attempts would often get Rito into trouble or erotic situations. Rito was sort of aware that Run likes him but never even consider it.
In To-Love-ru Darkness, Run is now a famous idol. She has also greatly matured around Rito and becomes closer to him on their date. During their date, Rito realizes that he hardly knows much about her. From this date Rito is now aware of how deep Run's feelings are towards him, but she is saddened with the fact that Rito would never see her as a real girl while sharing the same body with Ren. This was the case until Run and Ren reached "adulthood", causing them to split mind and body. Since then, Run is determined to try harder to gain Rito's affections.
Rito has begun to show more sympathy towards her feelings, going as far as considering her as a lover for the harem plan, but quickly shakes it off.
Run first met Kyouko when she starred as a villain in her show. At first, Run didn't take too kindly to Kyouko but after getting to know her better, Run sees that Kyouko is a really kind person who listens to Run's music and even reads her blog (and finding out that Kyouko is human/alien hybrid), and they became good friends. Kyouko knows about Run's feelings towards Rito and wishes the best of luck in getting him.
In To-Love-ru Darkness, Kyouko visits Sainan High and asked Rito to be her tour guide, intending to find out more about Rito for Run. When Rito saved her from a swarm of rampaging fans, Kyouko began to also develop feelings for him, something she has yet to tell Run.