From your screenshot, all the shortcut text is missing from the context menu entry (for example, Length... should have Ctrl+L next to it), so there may be something conflicting that caused the shortcuts to be deleted. Are there keyboard shortcuts listed when you right-click with other editing tools, such as the Edit tool, and do they work?
You can try resetting the shortcuts by going to the Customize menu > Customize Mode, click the Commands tab, and click the Keyboard button at the bottom. Go to the Editor category, click a command like Length, and see if there is currently a keyboard shortcut assigned.
Do you have any add-ins, code, scripts, or other applications installed? Otherwise, try renaming the normal.mxt, uninstalling any scripts, or possibly running a repair on ArcGIS.