Replicating styles with the Style Brush tool
Use this tool to replicate styles. When you first open OmniGraffle, the Style Brush tool is empty, and its cursor has arrows showing that you can absorb a style. Select it and click any object on the canvas to absorb the object's style into the brush. Once the brush contains a style, you can click any object to replace the object's style with the style in the brush. 
The tool's pop-up menu contains a list of styles that can be absorbed; select whichever ones you like, and the brush will only absorb or apply those styles. For example, if you only select Fill, you can apply a certain fill style to objects without affecting any of their other styles.
To reset the contents of the brush, select Clear Contents from the tool's pop-up menu; you can then absorb a new style. You can also Option-click a different object to replace the brush's contents.