Originally Posted by wardz
Try this: (Change Left to Right depending on direction you want)
/run if not MovePadFrame then UIParentLoadAddOn"Blizzard_MovePad"MovePadFrame:Hide()end
In case wardz excellent sollution (a macro you can place on a button to either mouseclick or keypress) isn't clear, there is a piece of the default UI that is not very known: the Mousepad; it puts a frame on screen with all the movements available (incl. strafe), each on a button that works like a toggle. IIRC the option to manually enable this is on the "Accessibility" menu of your Interface menu.
wardz sollution will activate the mousepad but keep it hidden (unless it was already active), and then click the button to turn strafe-left on/off.