Takeru and Nyaa-tan get along well with each other. Takeru is grateful for the kind things she does, even if he knows there are ulterior motives just to get his Sol/Lull. While Nyaa-tan at first might have used Takeru only for his Sol/Lull, she began to appreciate and cherish the time they spent together. She may have feelings for him but for the most part their relationship is more along the lines of close friends or even siblings.
Uri-tan and Nyaa-tan are very close and share an almost sister like bond. Uri-tan is Nyaa-tan's mentor in wisdom and does her best to guide Nyaa-tan in the right direction. Sometimes even if she has to literally knock sense into Nyaa-tan.
Uri-tan care for Nyaa-tan greatly. To the point where she even interfered in an official ETM12 match against Chu-tan, which had never been done by any other Eto prior.
Mo-tan loves Nyaa-tan and is not shy of showing and announcing it. She will physically accost Nyaa-tan every chance she gets. Mo-tan has a sock fetish and will do anything to get them from Nyaa-tan and will only take the ones that she has recently worn. Currently she has 67 of Nyaa-tan's socks and plans to sew them into a blanket.
Dora-tan is Nyaa-tan's mentor in spirital strength. She supports Nyaa-tan and would like to see her succeed in becoming a Zodiac. She is very adept in using Sol/Lull and has used it to build Nyaa-tan's home on Takeru's property and to transport them away from Chu-tan.
Nyaa-tan and Ki-tan haven't exactly interacted, but they both are mischievous and enjoy fooling around with each other (together with Inu-tan), and they are on good terms.
Same with Ki-tan, Inu-tan and Nyaa-tan gets along due their personalities and they are also on good terms with each other.
Piyo-tan and Nyaa-tan have a like-hate relationship. They sometimes gets along, but for the most part Piyo-tan, is on the receiving end of many of Nyaa-tan's pranks. Due Piyo-tan's short term memory loss she doesn't remember what Nyaa-tan has done but retains the underlying feeling of hatred towards her. Piyo-tan calls Nyaa-tan 'stupid cat'.
At one time Nyaa-tan and Chu-tan were very close friends. So much so that Nyaa-tan forfeited her chance at becoming a Zodiac in the first ETM12, even though she was favored to rank high so that she could help Chu-tan from behind the scenes. She traveled around taking care of problems for Chu-tan the world over but maintained the disguise of just being a care free trouble maker.
Nyaa-tan however regretted her choice as she saw Chu-tan becoming more and more distant and dark. She saw Chu-tan's Etotama being filled with negative energy and began to learn the forbidden Kagura Senguu technique to mend it. Nyaa-tan also decided to again strive to become a zodiac and relive Chu-tan of the responsibilities that were burdening her.
She challenged Chu-tan to a battle and attempted to use the Kagura Senguu technique on her. Unfortunately she was unable to complete the ritual and Chu-tan seeing it as a act of betrayal used the same technique on Nyaa-tan, destroying her Etotama.
Nyaa-tan survived and was able to reincarnate but with out most of her memories and only retaining her desire to become a Zodiac. Eventually she was able to regain her memories with the help of the other Zodiacs and Takeru. Nyaa-tan again faced off against Chu-tan and was able to succeed in expelling the negativity from her and healing Chu-tan's Etotama.
According to Aries-tan, Naya-tan has free time and time for teaching.