Non-intrusive measurement of current and voltage
have access only to the insulated exterior of the cable.


If all you got is the cable, then no.

You can use a current clamp meter around a wire. It measures the magnetic field created by the current inside the wire. But you can't use this around a cable, as the cable contains two wires with current going in opposite directions, which means their magnetic fields cancel. Whatever magnetic field there is to measure around the cable will depend more on its geometric properties than on the actual current.


  Can I (hopefully accurately) determine the direction of current flow


I'm going to pretend not to notice that this is AC and therefore current reverses direction 100/120 times per second. I think you meant the direction of power flow, which is from the utility to the load. Unfortunately, your cable contains two live wires (and maybe one Earth) and the current in both live wires goes in opposite directions since current always travels in a loop...

You can measure current by stripping the cable and getting to the wires. You don't need to strip the wires' insulation or cut them. Snap a current clamp around one wire and you can measure the current.

Measuring voltage without breaking the insulation is another challenge... What I usually do is to simply puncture the wire insulation with the tip of the multimeter probe. Of course after doing that the wire will no longer be waterproof, so it is only OK to use indoors.