Hm, burza z piorunami. From what I think burza itself includes that there were thunderbolts. Strong wind only - wichura from wicher (strong wind, normal wind is wiatr)
You could try to use Google Image to compare the meaning of the words (maybe it is not that personalized). I got:Polish ones:
burza - over 90% with thunderbolts (the number of lightnings is however much exaggerated, one would suffice) wichura - broken trees, rain, less than 5% of images had thunderbolts
Any kind of whirlwind are rather rare and are called trąba powietrzna. Usually they affect the area not bigger than a single place. Huragan (hurricane) appear in the news from USA. Tajfun (typhoon) - hm has it happened somewhere in Asia? The biggest thing in Poland is probably Orkan (I assume the name came from German).