Well, transformation is a frequently seen theme. The Diamond OCs might start off as one way but change throughout the story, either in terms of their physical form or their beliefs. Also, family and heritage play a role. Since the Diamonds have a complex family structure in 'Steven Universe', the OCs are often related to this in some way, and exploring their family ties and heritage can be a big part of the fanfiction.
One common theme is self - discovery. The OC often has to figure out who they are in the complex world of the Diamonds. Another theme is friendship, as they usually form bonds with the existing characters.
A major theme is power and its implications. The Diamond OCs often have unique powers, and the fanfictions explore how they use or misuse these powers. There's also the theme of acceptance. They may be different from the regular characters, and the stories show how they are either accepted or rejected. For example, some OCs face discrimination at first because of their differences but then find a place where they are welcomed.