Most of the MOA students have their special items that they are described to be carrying around in the Goddess Girls (Series).
Goddessgirls and goddesses
Aphrodite - Aphrodite is seen carrying a mirror around wherever she goes.
Ariadne - As described by Athena, Ariadne carries a glittery bag which contains wool in order for her to knit her long pink, sparkly scarf.
Artemis - Artemis is always carrying her bow and arrow. She puts it down next to her when she haves lunch. Sometimes, she brings her dogs around with her. In "Pandora The Curious", she was hand-carrying a small dog, because the "vain" bubble hit her. There, she was practically carrying everything Aphrodite would.
Athena - Athena is described by her carrying various different types of scrolls. However, in "Pandora The Curious", she was seen carrying makeup.
Hera - Sometimes, Hera can be wearing or holding various feathers or things to do with peacocks, her sacred animal which Aphrodite admires.
Iris - Not really described on what she holds in her hands regularly, Iris is seen on the cover photo of "Iris The Colorful" that she carries a jug with ancient paintings on it to bear water. MOA's messenger must bear water for the gods.
Godboys and gods
Ares - Ares is seen carrying a shield sometimes, since he is the godboy of war.
Hephaestus - Hephaestus is so weak, he needs a cane to walk.
Heracles - Heracles really loves carrying his club around. As described by everyone, that club can be quite annoying, and for most, extremely heavy. Athena was the only one who could convince Heracles to stop bringing it wherever he goes.
Theseus - Theseus newly carries his own weapon just like his cousin Heracles. As described by Apollo, he carries a sword that is rather small in the Olympian's eyes. Apollo describes it as a toy but Theseus carries it around with him anyways.
Zeus - Principal Zeus enjoys carrying thunderbolts around his belt or in his hands with him.