Soubu High School
When Iroha is introduced during her request it is shown that many other people in her grade pull pranks on her. During the series she isn't shown with other students in her grade and is mentioned to be the target of harassment from other girls due to her closeness with Hayama. She is not mentioned to have a best friend or to hang out with anyone.
Iroha first came to the Service Club with a request of losing the election but not in an embarrassing fashion. Later on Iroha makes herself at home in the club, spending possibly more time in the Service Club room than in her own council room.
After taking the position of president, she regularly visits the Service Club to ask them for favors or make some other request. Though her initial request has already been fulfilled, Hachiman feels a responsibility towards her since he pushed her to become the president, and so he puts up with her whims. She enjoys her time with the members as she may not have any other "friends".
Different from others, Iroha respects Hachiman and is very fond of him and calls him "senpai" in a somewhat playful manner. Despite her ways of keeping her image with others, she is shown to have no qualms about being seen with him in public even though he is an outcast in their school. Hachiman knows about her true personality and this makes her at ease. Thus she feels a lot more comfortable with him, she begins to admire him for his intelligence and presence of mind. She also likes his courage in revealing his feelings of desiring something genuine.
She was deeply moved by his desire to have something genuine. She is always surprised by his concern for her which is shown by her reactions during Hachiman's offer to carry her bags. She always seems to rely on Hachiman from the student council election to the Christmas celebration in collaboration with Kaihin Sougou High. When he refused to help her any further after that, she goes to the trouble of petitioning Shizuka Hiratsuka for getting Hachiman's help. It is hinted that Iroha may have developed feelings for Hachiman, due to their time together as she is often seen blushing in some of their interactions but its unknown what the true depths to them are.
Notably Hachiman treats her much like he does Komachi, unconsciously treating her in ways that he normally reserves for his little sister. He also feels a sense of responsibility towards her, due to his guilt over pushing her to become the president.
Interestingly, there are similarities in their personalities, Hachiman is especially wary of her and mentally grants her a "third grade Hikigaya certificate" for her ability to understand how his mind works. In Volume 10.5 (OVA Zoku/2), it is shown that Iroha went on a 'mock date' with Hachiman, where in spite of his lack of interest she ends up having fun with him even getting him to open up a little. Through this date, it is highly suggested she may be romantically interested in Hachiman rather than Hayama. She later uses the receipts from their date as blackmail material, much to his surprise. After their mock date, she "accidentally" shows his clubmates pictures of the date, leading to their quiet jealousy and Hachiman's embarrassment.
One of the running gags between the pair is Iroha misunderstanding Hachiman's words as an attempt to hit on her, followed by her quick apology and rejecting him. She has rejected Hachiman six times (up to season 2). This irritates him but very soon, he gets used to it and ignores her as he sends her on her way, which gets an irritation from her as well.
Hachiman says that he is annoyed by Iroha's foxiness but Iroha retaliates that he is the foxy one. Iroha is constantly taken back by Hachiman's kindness and his remembrance of her birthday.
For the Pre-Valentines event, she was surprised and seemed shocked when Kaori Orimoto asked Hachiman if she ever gave him handmade chocolate. After this, Iroha gave him some handmade chocolate as Hachiman was surprised that she seemed skilled in a kitchen. Sometime later, she seems to develop feelings for him and gets jealous when Hachiman speaks to other girls.
She is initially frightened by the latter's cold personality and harsh words, but gradually the two take a liking to one another. At one point, she comments that the bickering between Yukino and Hachiman about how to treat her resembled a lecture from her parents. Whether Iroha's interest seemingly shifted from Hayato or knowing the rumors to be false, Iroha doesn't seem to be bothered by the rumor of Hayato and Yukino being a couple.
Later in the novels, Iroha's interactions with Hachiman appear to bring about a spark of jealousy from Yukino since Hachiman and Iroha spend a lot of time together.
However, Yukino seems to have a soft spot much akin to the one she has for Yuigahama, and pampers Iroha somewhat due to her desire to be a good upperclassman.
She has a good relationship with her, they call each-other by their first name. They were only acquaintances through their mutual connection with Hayato Hayama, prior to Iroha's request.
As Iroha becomes a more frequent guest to the Service Club, the two become noticeably more familiar with one another. Just like Yukino, Yui can become jealous or uneasy of Iroha's closeness to Hachiman.
Student CouncilIroha's initial interactions with the student council members are awkward. Since Iroha is younger and she pretends to be an air head. She is also uncomfortable with her position as Student Council President.
After the completion of the Christmas Event she gains confidence and comfort with the other student council members. She asked the vice president for date spots for her mock date with Hachiman.
She was willing to help Iroha after the election with student council works but Iroha likes to keep her distance from Meguri due to her dealing with college exams. Though Hachiman feels that Meguri's natural air headed personality is intimidating to Iroha who pretends to be an airhead as part of her persona.
StudentsEpisode 10 of Season 2 (adapted from Volume 9 of light novel) she gathered the courage to confess to him in Destinyland, after being influenced by Hachiman's desire for genuine things, but she was rejected.
Hayama later confiding with Hachiman that he rejected her because her true feelings were probably for another person rather than him. They are still on good terms despite the rejection. Iroha once interviewed Hayato for the school newspaper in Volume 10. Iroha still tries to impress Hayama. In Episode 12 of Season 2, Iroha gave pre-Valentine chocolate to Hayama.
After realizing she will never be loved by Hayama, she seemingly stopped flirting with him and started to flirt with Hachiman instead.
Shizuka watches over Iroha like she does with all other students. Iroha mentions she takes advice from Shizuka from time to time. In the light novel, Shizuka tried to stand-up for Iroha against her class teacher for the student council candidacy after realizing that it was a prank by her peers. Shizuka is the teacher in charge of all the events that are headed by Iroha, like the Christmas collaboration event, the pre-Valentine event, etc.
Once Hachiman refused to help Iroha with her student council work, Iroha went through the trouble of asking Shizuka for Hachiman's help as a student council order.
Later Iroha manages to use her experience to manipulate him and his student council resources for her own gains. They collaborated on the Christmas and Pre-Valentines events.
They made their acquaintance during the Christmas collaboration event. Even though they have seen each-other during the double date (Hayama, Hachiman, Kaori, Chika), they couldn't recognize each other which Hachiman thinks is a good thing.
Later in the series, Iroha is with Hachiman and Kaori and asks about their middle school relationship. Hachiman mentions "stuff happened in the past", which Kaori confirms but doesn't elaborate onto her. Iroha seems very interested in their relationship.
In the light novel, Iroha tried to appeal to Haruno and was trying to get in the good graces of an influential person. Haruno was able to see through her facade, but goes along with it anyway. Iroha personally told Hachiman how scary Haruno is.
In Episode 12 of Season 2, Iroha invited Haruno as an instructor for the pre-Valentine collaboration event at the community centre. It is likely they have exchanged their contacts.