Placing graphics inside a shape with the Image inspector
You can use this inspector to position an image inside a shape. (Note that instead of creating an object and then adding an image, you could also simply drag an image file from another application straight onto the canvas.)
Use the Image pop-up menu to set an image in the selected shape. Once an image is set, a Remove Image command appears in the menu. When you browse for an image file, you have the option of creating an alias (or "link") to the image instead of adding the image to the OmniGraffle file itself. If you do this, the OmniGraffle document depends on the original image file; the alias will not work if you delete the image file or open the document on a different computer. If an object's image comes from an alias, some extra commands become available in the Image pop-up menu: you can Open the original image file, Reveal the original file in the Finder, or stop using the alias and Embed a copy of the image in the OmniGraffle document.
Another way to set an image is just to drag an image file from another application and drop it on the image well, or on the shape object itself. 
The first button displays the image at its natural aspect ratio, with a zoom level and position as set with the controls below. The second button makes the image stretch to fit inside the object. The third button makes the imae tile indefinitely across the object. 
The positioning offsets are enabled if you are displaying the image at its natural aspect ratio, as set by the first of the three buttons above. You can type a positive or negative percentage, or just drag the image around in the image well to indicate the area you want. 
The zoom controls are available unless you are stretching the image to fit the shape. You can enter a zoom percentage, or just drag the slider, to make the image larger or smaller. 
You can make the image transparent and let the object's fill show through by decreasing the value of the opacity field, or by dragging the opacity slider. You can also add an image to a canvas. Just click the canvas in the sidebar (so that it becomes highlighted in your selection color), then use the Image inspector normally.