As an added bonus for iOS 9 users, you don’t have to worry about trying to memorize the keyboard shortcuts, because OmniGraffle presents them to you whenever you hold down the Command (⌘) key on your Bluetooth keyboard. The basic list of keyboard shortcuts is shown when you don’t have anything selected on the canvas:

And if you do have something selected on the canvas, the shortcut overlay offers a few extra keyboard shortcuts that you can use.

Command	Keyboard Shortcut
Cut	Command-X
Copy	Command-C
Duplicate	Command-D
Paste	Command-V
Copy Style	Option-Command-C
Paste Style	Option-Command-V
Group	Shift-Command-G
Ungroup	Shift-Command-U
Select all	Command-A
Undo	Command-Z
Redo	Shift-Command-Z
Delete (selected object)	Delete
New Canvas	Option-Command-N
Previous Canvas	Command-↑
Next Canvas	Command-↓
Close Current Document	Command-W
Select All	Command-A
Lock	Command-L
Unlock	Option-Command-L
Bring to Front	Shift-Command-F
Bring Forward	Option-Command-F
Send to Back	Shift-Command-B
Send Backward	Option-Command-B
Enter/Exit Full Screen	Control-Shift-F
The following keyboard shortcut only works when viewing the contents of a folder in the Document Browser.
New Document	Command-N