PC-12 pilot reported encountering severe turbulence and inflight icing that resulted in large altitude excursions.

Narrative

I was flying a part 91 leg when the Controller informed me of heavy precipitation about 10 miles ahead and to let them know if I needed deviations. I was just entering IMC and could see that at my assigned altitude of 16000msl I would be fairly near the tops. I had filed for 180 but due to the low altimeter settings it was not available so accepted 160. I begin considered asking for higher and deviations while the radar was warming up. The satellite weather showed several small cells right and left of me. With the ones to the right indicating lightning and the storms trending east. I wasn't in IMC more than a minute when I was struck by lightning and it appeared to strike the propeller though I can't be sure. I immediately requested deviations and received them slowing as I was troubleshooting the aircraft for damage from the strike. With no breakers popped; radios still functioning; and power plant; controls; autopilot and avionics appearing normal I was prepared to deviate. Radar started signaling and wasn't showing anything directly in front of me. At that moment severe turbulence began disengaging the autopilot and severely moving the aircraft up and down. I further reduced power and told ATC I would be unable to maintain altitude. They gave me full lateral and horizontal authority. I began a climb knowing the tops were not far above letting ATC know my intentions. Initially I was climbing well and then the climb slowed tremendously. I noted lite rime and started boots and prop heat; which both worked as expected. I broke out at 18300. And requested 20000msl and received it. Further pilot reports were given after incident and the rest of the flight went without incident. I stayed above the weather as long as possible and had light turbulence on the way back down which quit as soon as I was under the bottoms.Suggestions: Don't assume because you're near the tops severe weather won't happen. Don't trust satellite Wx reports. Don't assume because cells are small they won't pack a punch. Start radar earlier.