Nuclear bombs. These are the only weapons of mass destruction on earth. The effects of a nuclear bomb are heat, blast, EMP, and radiation. If you see a bright flash of light like the sun, where the sun isn't, fall to the ground! The heat will be over in a second. Then there will be two blast waves, one out going, and one on it's way back. Don't stand up to see what happened after the first wave; anything that's going to happen will have happened in two full minutes. These will be low yield devices and will not level whole cities. If you live through the heat, blast, and initial burst of radiation, you'll probably live for a very very long time. Radiation will not create fifty foot tall women, or giant ants and grasshoppers the size of tanks. These will be at the most 1 kiloton bombs; that's the equivalent of 1,000 tons of TNT.
Here's the real deal, flying debris and radiation will kill a lot of exposed (not all!) people within a half mile of the blast. Under perfect conditions this is about a half mile circle of death and destruction, but, when it's done it's done. EMP stands for Electro Magnetic Pulse and it will fry every electronic device for a good distance, it's impossible to say what and how far but probably not over a couple of miles from ground zero is a good guess. Cars, cell phones, computers, ATMs, you name it, all will be out of order.
There are lots of kinds of radiation, you only need to worry about three, the others you have lived with for years. You need to worry about "Ionizing radiation," these are little sub atomic particles that go whizzing along at the speed of light. They hit individual cells in your body, kill the nucleus and keep on going. That's how you get radiation poisoning, you have so many dead cells in your body that the decaying cells poison you. It's the same as people getting radiation treatments for cancer, only a bigger area gets radiated. The good news is you don't have to just sit there and take it, and there's lots you can do rather than panic.
First; your skin will stop alpha particles, a page of a newspaper or your clothing will stop beta particles, you just gotta try and avoid inhaling dust that's contaminated with atoms that are emitting these things and you'll be generally safe from them. Gamma rays are particles that travel like rays and they create the same damage as alpha and beta particles, only they keep going and kill lots of cells as they go all the way through your body. It takes a lot to stop these things, lots of dense material, on the other hand it takes a lot of this to kill you. Your defense is as always to not panic. Basic hygiene and normal preparation are your friends. All canned or frozen food is safe to eat. The radiation poisoning will not effect plants so fruits and vegetables are OK if there's no dust on 'em (rinse 'em off if there is). If you don't have running water and you need to collect rain water or use water from wherever, just let it sit for thirty minutes and skim off the water gently from the top. The dust with the bad stuff in it will settle and the remaining water can be used for the toilet which will still work if you have a bucket of water to pour in the tank.