The exact translation for the word tornado is "windhose(singular)", but this includes all forms of rotating air, moisture, and clouds with an visible vortex on the ground--and don't have to be damaging. This means that tornadoes, waterspouts, and dust devils are all "windhosen(plural)". You can differentiate between a small "kleine windhosen(plural)" and large "große windhosen". So the more accurate word for a tornado which is damaging is "tornado or tromben(ital.)".
There is the word "wirbelsturm" which includes hurricane, typhoons, cyclones and also tornadoes but not waterspouts (wasserhosen) and dustdevils. The German word "wirbel" alludes to all forms of rotating air or clouds. Sturm(singular), stürme(plural), or orkan(singular), orkane(plural) means a really severe thunderstorm with hail, heavy lightning and so on. A normal thunderstorm is called a "gewitter(singular and plural)".

So, in summary:
tornado=large "windhose/windhosen or trombe/tromben"
dust devil="sandteufel or sandwirbel"
waterspout="wasserhose/wasserhosen"
thunderstorm="gewitter"
severe thunderstorm="sturm/stürme (over 20m/sec) or orkan(over 32m/sec)"
hurricane, cyclone, or typhoon="wirbelsturm/wirbelstürme"