The dash lights and number plate lights are fed from one side of the sidelight circuit, so one side should work.
So out with the metre first, as you know you are getting 1 power FEED at the light switch stalk.
Therefore at least one side of the sidelight circuit is fine, assume the front sidelight on the good side works as well.
You may have just got a few blown bulbs, odd but it does happen if the alternator spikes as they can do, only ever had it once myself on a mini, blew the headlight bulbs but no others!!
I would check for power at the front/rear side tailights, then look for a FEED to the stalk from the ignition, that is ONLY live when the ignition is in position 2, as if this is missing the HEADLIGHTS will not switch on, this is what prevents the lights from accidentally being left on when you switch the car off.
tabetha