Miyuri and Mafuyu have a bitter relationship at the start of the series. Miyuri bullied and tormented her and Tomo. The anime adds a reason for this behavior. When they were children, she told Mafuyu that she believed ESPers exist, but Mafuyu told her otherwise, embarrassing Miyuri in front of the other kids. After the incident with the Russian mercenary group, she begins to show more care for Mafuyu and their classmates.
As explained above, Miyuri has bullied Tomo as well. In the manga, she seems to torment Tomo more, the latter's family having been competing since the Taisho period of Japan. In the anime, her dislike of Tomo seems to be due Tomo having a larger bust than her. Like with Mafuyu, Miyuri lightens her treatment of Tomo, but this is only seen in the anime's second season.
Miyuri loves Katja dearly, and treats her like her own littler sister.