Edit menu
Undo — OmniGraffle remembers a list of changes you make to a document. Choose this command to move one step backwards in the list, as if you hadn't done the last thing in the list. Keep choosing it to keep stepping backwards in time.
Redo — If the last thing you did was to Undo something, you can step forward and do it again, effectively Undoing the Undo.
Cut — Remove the current selection and put it on the clipboard, so you can paste it somewhere else.
Copy — Copy the current selection to the clipboard.
Copy As
PDF — Put a PDF copy of the current selection on the clipboard, for pasting into any application that understands PDF. If the application you paste into also supports LinkBack (this includes OmniGraffle itself), you can even go back and edit the pasted content in OmniGraffle.
TIFF — Put a TIFF copy of the current selection on the clipboard, for pasting into any application that understands TIFF.
Vector PICT — Put a Vector PICT copy of the current selection on the clipboard, for pasting into any application that understands Vector PICT (this is especially useful for pasting into Microsoft Word, which has a curious bug that prevents it from getting the right data when you paste in OmniGraffle content with the ordinary Copy command).
AppleScript — Put an AppleScript representation of the selected objects on the clipboard. You can paste the result into Script Editor or into the Action inspector of another object to make a script that recreates the objects. The output is also useful just for studying how OmniGraffle's AppleScript support works.
Paste — Place the contents of the clipboard on the canvas, at the last place you clicked with the Selection tool. (or insert text from the clipboard if you are editing an object's text). If there is an image or some text in the clipboard, a new shape object containing the image or text is created.
Paste and Match Style — When you are editing text, you can use this command to paste in some text without bringing along the style it had in the application you copied it from. Instead, it matches the style of the text you already have, as if you had typed it there yourself.
Duplicate — Make a copy of the current selection and place it on the canvas, without using the clipboard.
This command has a special feature:
Select something on the canvas and Duplicate it.
Use the Selection tool to move the copy; OmniGraffle learns the distance and direction of the copy in relation to the original.
Duplicate again as many times as you like; each new copy is the same distance and direction from the previous copy.
Delete — Obliterate the current selection, forever banishing it from this plane of existence (unless you Undo).
Select All — Select everything selectable on the canvas. Remember that objects on locked layers can't be selected. If you are editing the text of an object, this instead selects all of the object's text.
Select
Similar Objects — Select all of the objects on the canvas that have the same style attributes as the currently selected objects.
Connected Objects — Select all shapes that are directly or indirectly connected by lines to the currently selected objects, and all of the lines between.
Ancestor Objects — Select all of the ancestors of the currently selected objects, based on the hierarchy established by connection lines.
Descendant Objects — Select all of the descendants of the currently selected objects, based on the hierarchy established by connection lines.
Outlining — The commands in this sub-menu (and their keyboard shortcuts in particular) make it easier to work quickly in the outline view. They are only available when the outline view is open and you have an active selection in it.
Mouseless Editing — These commands are most useful when you invoke their keyboard shortcuts; you can do a whole lot without even touching the mouse.
Select Shape — These commands select a shape based on its position relative to the currently selected shape.
Create Shape — These commands make a new shape relative to the currently selected shape.
Canvases
New Canvas — Add a new canvas to the document.
Duplicate Canvas — Add a new canvas, identical to the current canvas, to the document.
Delete Canvas — Get rid of the current canvas completely.
Layers
New Layer — Add a new layer to the current canvas.
New Shared Layer — Add a new shared layer to the current canvas.
Duplicate Layer — Add a new layer, identical to the selected layer, to the canvas.
Merge Layer Down — Move everything on the selected layer to the next layer down, then delete the selected layer.
Delete Layer — Get rid of the current layer completely. You can't delete the last layer in a canvas.
Delete All Copies — This command is only available when you select a shared layer. It deletes all instances of the shared layer on any canvas throughout the document.
Layer Settings — These commands replicate the clickable icons on a layer in the canvases sidebar. Visible shows or hides objects on the layer, Printable controls whether objects on the layer should be included when printing, and Unlocked controls whether objects on the layer can be selected or edited.
Select All In Layer — Select all of the objects on the selected layer.
Move Selection To Layer — Move all selected objects to the selected layer.
Tables
Insert Row — When you have one cell of a table selected, choose this command to add a new row of cells to the table. The new row appears immediately before the row containing the selected cell.
Insert Column — When you have one cell of a table selected, choose this command to add a new column of cells to the table. The new row appears immediately before the row containing the selected cell.
Select Row — When you have one cell of a table selected, choose this command to select the entire row that contains the cell.
Select Column — When you have one cell of a table selected, choose this command to select the entire column that contains the cell.
Magnets
Copy Magnets — Put the magnet arrangement of the selected object onto the clipboard, so that you can paste them to a different object.
Paste Magnets — If there is a magnet arrangement on the clipboard, apply it to the selected object. Any existing magnets are replaced by the new ones.
Delete Magnets — Get rid of all the magnets on the selected objects.
Shapes
Subtract Shapes — Take the selected shapes and use the front shapes to punch a hole in the back-most shape. You can reorder shapes with the Bring/Send commands in the Arrange menu. 
Union Shapes — Combine two or more selected shapes, eliminating internal lines to make a single solid shape. 
Intersect Shapes — Create a shape from the overlapping areas of the selected shapes. 
Find
Find — This summons OmniGraffle's Find panel. You can search for a specific string of text, or you can use a regular expression to match a whole class of strings. When searching for a specific string, select Ignore Case to match letters regardless of whether they are uppercase or lowercase; select Whole Word to avoid matching portions of a word. If you use groups in a regular expression, you might want to select (or replace) the whole expression, or just one of the groups; use the pop-up menu to indicate which. For the purposes of Previous and Next, OmniGraffle considers objects in left-to-right, top-to-bottom order.
Find Next — Choose this to find the next occurrence of the text you last entered in the Find panel, as if you had just clicked its Next button.
Find Previous — Choose this to find the previous occurrence of the string you last entered in the Find panel, as if you had just clicked its Previous button.
Enter Selection — Select some text in an object, then choose this command to put the selected text into the Find panel, replacing whatever was there before. Then you can use the Find Next and Find Previous commands to search for other occurrences of the text.
Scroll to Selection — Move the view so that the selected objects are visible.
Spelling and Grammar
This submenu contains Mac OS X's standard spelling and grammar utilities. For the purposes of Previous and Next, OmniGraffle considers objects in left-to-right, top-to-bottom order.
Insert Variable
While you are editing a shape object's text, choose one of these commands to insert a special tag. When you finish editing the text, the tag changes to represent some aspect of the object itself, the canvas, the page, or the document. If the data that the tag refers to changes, the tag automatically updates itself. Some variables, like Page Number, are useful for putting on a shared layer and then sharing that layer with every canvas.
If you are using one of the date variables, you can customize the format of the date using Cocoa's date formatting tokens. For example, to get a date like "2005 - 10 - 06 16:00", you could type this:
<%date %Y - %m - %d %H:%M %>
Canvas Name — the name of the canvas the object inhabits.
Document Name — the name of the document the object inhabits.
Current Date — the date right this very minute; this is nice for knowing when a document was printed.
Document Creation Date — the date that the document was originally created, according to Mac OS X's file system.
Document Modification Date — the date that the document was last saved, according to Mac OS X's file system.
Creator — the name of the user who created the file, according to Mac OS X's file system.
Modifier — the name of the user who last saved the file, according to Mac OS X's file system.
Page Number — the number of the page that the object inhabits, based on settings in the Canvas Size inspector and the Page Setup panel.
Total Pages — the number of pages in the whole document. Use this with the Page Number tag to get results like "Page 2 of 5".
X Position — the object's horizontal distance from the origin, just like in the Geometry inspector.
Y Position — the object's vertical distance from the origin, just like in the Geometry inspector.
Width — the object's horizontal size, just like in the Geometry inspector.
Height — the object's vertical size, just like in the Geometry inspector.
Line Length — This tag is somewhat unique. If the shape containing the tag is a line label, it shows the line's length. It's not useful if the shape object is not attached to a line.
Edit LinkBack item — If you have pasted LinkBack content from another application, select the object and use this command to open the content in the original application.
Special Characters — Summon the standard Mac OS X Character Palette.