Despite her non sequiturs and a tendency to nod off during lectures which upset her teacher, Yukari Tanizaki, she remains in Yukari's homeroom class for all three years. Because of her poor performance on exams, she is a member of the "Bonkurazu" (translated as "Knuckleheads" or "Bonkers" in the anime and "Numbnuts" in the manga). Her decision, on Chiyo's advice, to seek a teaching career after graduation is viewed by Yukari as a deep personal insult.
Osaka often acts like a "space cadet": slow, inattentive, and stuck in her own world. Although she seems slow and easily distracted, she merely has a mind that works quite differently from that of most people. This makes her prone to daydreaming, absentmindedness, and non-sequiturs, but it also makes her unusually good at answering certain types of riddles. But while some people assume that she lacks focus, the truth is that in quite a few cases, Osaka is really a little too focused. When she daydreams in class she tends to dream about Chiyo and her pigtails either controlling her, giving her the ability to fly, keeping her alive, or replacing them with new ones. When she gets a thought in her head, she tends to focus on it so intently that the rest of the world simply disappears, causing her to often miss what's going on around her (an example is episode 2, when Osaka was focused on eye floaters when a cockroach invades the class and Tomo was enthusiastically and noisily trying to exterminate the bug, literally sending desks, and presumably students, flying). During a vacation with her friends, she had the idea to wake Miss Yukari by banging a frying pan, but, in her drowsiness, took a butcher knife from the kitchen instead. She is especially close to Chiyo, since even though Chiyo gets much better grades, both are bad at P.E. (Osaka is unusually stiff, even when stretching out, shown on multiple occasions to not be able to reach her toes even with Chiyo pushing her), and both seem to approach the world with the same sense of childlike wonder and curiosity, though Chiyo's is usually tempered by common sense and information, while Osaka's is not. In fact, Chiyo provides this for her, habitually reaching to grab Osaka's shirt sleeve when Osaka begins to muse about doing potentially dangerous things, and presumably might follow through if not restrained and "brought back to earth."
In contrast to most of her peers, Osaka always keeps a quiet, accessible mood. It's extremely rare to catch her in a fit of anger or losing control (as seen in the January chapters of Vol. 4 of the manga or Episode 25 of the anime, when she sports a maniac grin after finally learning how to break a pair of chopsticks evenly, and gets mad at Tomo for not doing it properly).
Osaka has been known to use the phrase "O-ha!" (short for おはよう, ohayou, "good morning"), which was popularized by Shingo Katori of the pop group SMAP, as an example of how "normal" Japanese people talk. As Tomo points out, this is not a correct assumption.
At the same time, Osaka has a habit of being able to point out obvious things nobody else seems to notice (such as the fact that none of her core group of friends has boyfriends) and has surprising levels of knowledge on unexpected topics such as marine biology and obscure kanji. She also seems to have a strange obsession with sea slugs. In the anime, she was also every bit as interested as the other girls to hear what Nyamo had to say about sex. However, her sense of humor is sometimes unusually morbid. On their first trip to Chiyo's summer home, Osaka proposed telling a scary story where all of the girls are murdered one by one, only to reveal that in the end, she was the one who killed them all. When the other girls couldn't decide between a haunted house, a cafe, and stuffed animals as their theme for the second-year Culture Festival, she suggested a cafe full of cat corpses as a compromise. She is also easily amused by things that most people would consider bizarre. During the Sports Festival, she made a big deal out of running the obstacle course because she thought the event of sticking her face in flour to get a candy was funny and had a giggle fit when she got there, and well afterwards, her face still covered in flour. The manga also revealed that she actually likes to run outside and play in typhoons, yet is easily spooked by thunder.
Osaka's real given name means to walk or to go on foot and her surname means spring day.