I REALLY recommend that you start with some of the search engines for kids and library resources rather than going directly to Google.
General Sites for Extreme Weather
Weather Storm Encyclopedia - http://dw.weather.com/encyclopedia/
Weather WizKids - http://www.weatherwizkids.com/
Web Weather for Kids - http://eo.ucar.edu/webweather/
Severe Weather - http://weather.about.com/od/thunderstormsandlightning/u/severestorms.htm
Climate Extremes and Weather Events - http://lwf.ncdc.noaa.gov/oa/climate/severeweather/extremes.html
Natural Disaster - http://www.factmonster.com/ipka/A0775896.html
Danger Zone - Natural Disasters - http://wayback.archive-it.org/3635/20130906075458/http://library.thinkquest.org/03oct/01352/index2.html
FEMA - http://www.ready.gov/be-informed
National Geographic - Natural Disasters - http://environment.nationalgeographic.com/environment/natural-disasters/
Preparing for Disasters - http://www.libertymutual.com/claims-insurance/catastrophes-natural-disasters/preparedness?keyCode=ISCMM0GB&src=lmcm-s-ggl-brd201310100079c
Drought:
Drought Information for Kids - http://www.state.nj.us/drbc/hydrological/drought/4kids/
Drought for Kids - http://drought.unl.edu/droughtforkids.aspx
All About Droughts - http://www.wrh.noaa.gov/fgz/science/drought.php?wfo=fgz
Drought - http://www.ready.gov/drought
Sandstorm
Sandstorms from Info Please - http://www.infoplease.com/ce6/weather/A0843423.html
All About Sandstorms - http://easyscienceforkids.com/all-about-sandstorms/
Sandstorm Safety Tips - http://www.nws.noaa.gov/om/brochures/duststrm.htm
Cyclone
Cyclone Facts for Kids - http://www.ehow.com/info_8623017_cyclone-kids.html
How to Prepare for A Cylclone - http://www.bom.gov.au/cyclone/about/tc-checklist.shtml
Heat Wave
About Heat Waves - http://www.nws.noaa.gov/om/heat/index.shtml
Heat Waves - http://www.absoluteastronomy.com/topics/Heat_wave
Coping with a Heat Wave - http://www.disastercenter.com/guide/heat.html
Typhoon
What Causes Typhoons - http://www.tropicalweather.net/what_causes_typhoons.htm
Hurricanes and Typhoons - http://www.aoml.noaa.gov/hrd/tcfaq/tcfaqHED.html
Safety Tips - http://japan.usembassy.gov/e/acs/tacs-typhoon.html
Monsoon
Monsoon, Forces of Nature - http://library.thinkquest.org/C003603/english/monsoons/index.shtml
What is A Monsoon - http://weather.about.com/od/monsoons/f/monsoons.htm
How to Prepar for a Monsoon - http://www.monsoonsafety.org/safety-prep/
Hailstorm
Driving in a Hailstorm - https://www.progressive.com/vehicle-resources/hail-driving/
How to Prepare for a Hailstorm - http://www.statefarm.com/learning/disasters/learning_disas_hail.asp
Blizzards and Hailstorms - http://www.factmonster.com/ipka/A0768992.html
Hailstorms and Hail Damage - https://stormdamagecenter.org/hail-storm.php
Tsunami
National Weather Service - http://itic.ioc-unesco.org/index.php?option=com_content&view=article&id=1169&Itemid=2017
About Tsunamis - http://www.statefarm.com/learning/disasters/learning_disas_tsunami.asp
Blizzard
Tips from the Red Cross - http://www.redcross.org/prepare/disaster/winter-storm
NOAA -http://www.wrh.noaa.gov/fgz/science/blizzard.php?wfo=fgz
Blizzards -http://www.ussartf.org/blizzards.htm
Blizzard -http://www.kidskonnect.com/subjectindex/15-educational/science/64-blizzard.html