Editing connection lines and shape edges with the Lines and Shapes inspector
Use the Lines and Shapes inspector to change the appearance of the selected connection lines or of the line drawn around the edge of the selected shapes.
The Stroke checkbox determines whether the path of the connection line or the outside of the shape should be traced with a stroke at all. When it is selected, controls become available for changing the appearance of the stroke. 
Two buttons determine whether to draw a single stroke or a double stroke. 
Click the color well to choose a color for the stroke. 
Enter a number in the Thickness field or use the arrow buttons next to it to choose how thick the stroke should be. 
Use the Corner Radius field to set how round the corners of the shape or line should be; enter 0 for perfectly pointy corners. 
The first of the three pop-up menus determines the stroke pattern (solid, dashed, dotted, et cetera). The center pop-up menu determines how the stroke appears at its ends: The Butt option ends the line by cutting across its endpoint at an angle perpendicular to the line itself, while the Round and Square options let the line extend past its endpoint based on the stroke width. The third pop-up menu determines how the stroke appears at its corners: Miter creates a sharp corner, Round creates a soft corner, and Bevel creates a cut-off corner. 
The bottom section changes depending on what kind of object you have selected. If you have a shape object selected:
A grid containing the available shapes appears. It includes all of OmniGraffle's built-in shapes plus all of the current canvas's custom shapes (ones created with the pen tool or shape combinations).
If you have a connection line selected:
The three pop-up menus determine the style of the tail, middle, and head of the line. Use the tail and head menus to set the line endings. Use the middle menu to set how the line travels from its source to its destination: Straight for a line that takes the shortest possible path between points, Curved for a line that turns smoothly to pass through each point, Orthogonal for a line that always travels horizontally or vertically, or Bezier for a line with control points you can adjust with the selection tool.
Use the fields below the tail and head menus to change the line ending sizes. Click the reverse button to swap the line's source and destination points.
Click Remove Midpoints to get rid of all points between the source and destination points.
The Line Hops menu determines what the line should do when it crosses other lines; choose one of the hop types to make the line jump over or under other lines, or choose Ignore this line to prevent other lines from hopping over or under it. The hops depend on the ordering of the lines involved; you can reorder objects with the Bring and Send commands in the Arrange menu.
You can also edit the stroke of a canvas itself. Just click the canvas in the sidebar (so that it becomes highlighted in your selection color), then use the enabled controls in the Stroke inspector.