Weapons of mass destruction fall into three large categories.
First we will consider what are called, usually incorrectly, 'poison gases'.
One first thinks of 'gas masks'. They are not 'gas masks' at all. They are particulate filters.
One true and actual 'poison gas' is chlorine. Just ordinary chlorine that is used to sanitize drinking water. It is evil stuff if not extremely diluted and dissolved in water. 'Gas masks' are useless against it, because it is NOT a particulate, it is an actual gas. The filters in a gas mask cannot capture it.
Cylinders of the stuff, under pressure, can and have broken, been damaged, or otherwise allowed to vent their contents to the air. The result is described as a yellow-green fog or cloud. Should you encounter such a thing, from an accident at a large swimming pool, or a water or sewage treatment facility, or some industrial accident, depart the area at 90 degrees to the wind. 'Crossways', in other words.
It is heavy, and lays close to the ground. It moves with the wind, and is (eventually, sooner or later) diluted and eventually dispersed by the wind. It burns your lungs and airways and eyes. It will also burn skin, but if it is strong enough to burn skin, your lungs are in real trouble.
Terrorists have discovered that this is the poor man's 'chemical weapon' of choice. It has been used against US troops in Iraq.
The remaining 'chemical weapons' or 'poison gases' are in fact almost always a finely divided particulate or droplets.
Tear gas (CN or CS) are examples of particulate-dispersed chemical weapons. The typical means of dispersing them is to impregnate an intentionally flammable chemical mix, similar to matchhead material, called 'smoke mix', for it's characteristic of burning in a fashion to produce a huge amount of smoke. This smoke is tiny particles. The chemical agent adheres to these tiny particles and are inhaled or land on the skin causing great discomfort... or worse. 'Tear gas' can kill you.
'Gas masks' work effectively on this class of materials, since it is a small particulate. The filters capture it and allow air to pass on by, slowly clogging the gas mask filters. Exit the area as soon as possible. Further, exposed skin, particularly with CS, will be greatly irritated. Long sleeves help. Covering all exposed skin helps. Covering the skin with vaseline helps.
Even breathing through a rag or t-shirt dampened with vinegar helps, for the vinegar dissolves the active portion of the agent sticking to the tiny particles.
Another smoke-dispersed chemical agent is called BZ. This is a super-hallucinogen, a super-LSD, and in very heavy doses be lethal. The lethal amount is actually quite small, but its dispersal in smoke means that to get enough to kill you, you have to breathe a huge amount of the smoke.
Standard 'gas masks', filter-masks, are also effective against this stuff. Exit the area immediately.
Sarin 'gas', also known as 'GB', is ugly stuff. Think of it as a 'pesticide' designed to kill humans. It is typically a liquid, and is dispersed in a weaponized military application by a small 'bursting charge', which turns the liquid into a mass of finely divided droplets. Standard 'gas masks', filter masks, are effective against this stuff. Exit the area immediately.
Another chemical agent, perhaps the most dangerous and most lethal, is called 'VX'. It is uniformly lethal to those exposed without the almost instantaneous administration of an injected chemical antidote, physostigmine and atropine, or similar chemicals. Most civilians simply do not have access to that. It is lethal upon inhalation of the infinitesimal droplets, and has the additional hazard of going right through exposed skin into the blood. In an area where this stuff is released, by the same means as GB or Sarin, a liquid dispersed by an explosive bursting charge, you cannot touch anything and you need protective outerwear in addition to the 'gas mask'.or filter mask.
Like the insecticides which they resemble, they are useful only where they are deployed. They do not travel very far. They are local area weapons. The most effective means of defense is to simply avoid the area.
Biological weapons, weaponized anthrax spores, for instance, are a different matter. There is little indication that you are being exposed. The only real defense is standard 'anti-infection' procedures. Wear glasses, don't touch your face and particularly not your eyes or your mouth without thorough soap-and-water cleaning of your hands. Once an infected population is established, it is self propagating, and is far more dangerous thereby than chemical weapons, which are by their nature a localized hazard.
The heavies are nuclear weapons. They are immensely powerful, with an immediate blast radius measured potentially in miles. Anything inside that blast radius is immediately atomized.
The immediate blast produces a huge amount of neutrons, which are subatomic, heavy particles, which are hugely penetrating. They are responsible for the majority of fallout from nuclear blasts. Physical material, dirt, steel, concrete, and the like are irradiated by these neutrons, and become themselves radioactive. Neutrons are the only means of causing other material to become radioactive. The irradiation by neutrons causes these other items to become radioactive, they are drawn up into the mushroom cloud, and become irradiated and actively begin to emit alpha, beta, or gamma.
Alpha is easily stopped by paper or skin. Breathing in a particle, however, can cause a lung cancer to develop. Beta is a bit stronger, but it too is stopped by minimal shielding.
Gamma is very penetrative, and requires serious shielding. Most fallout, thankfully, is fairly short lived. A few days, and several half-lives occur, and the emitted radiation falls away to almost nothing. You do not want to track these radioactive particles of fallout into your sheltering place, no matter where that is. Don't go out
unless you absolutely have to, and leave clothing at the door, including shoes.
The heaviest fallout of the strongest kind will be closest to the blast. Don't worry about neutrons.... to receive neutrons, you have to be line of sight to the explosion, and in that case, you are pretty much dead anyway, unless you are deep underground.
Gamma is going to be more present in particles which are heaviest and thus closest to the blast point. The half lives will be longer. The further you go away from the blast, the more the fallout will be alpha and beta.
In addition to the 'grades' or 'degrees' of harmful particles-- again, don't worry about neutrons-- if you get any at all you are likely dead anyway-- but gamma us worst, and its sources are longest lived; beta is midrange, and alpha is shortest livied and most easily stopped.
The other rules of radiation are time, distance, and shielding. The less time you are exposed, the more distance there is to the source, and the more shielding you have from the source, the better your chances for survival.
After a fallout event, stored food and water will be fine. Crops in the field will have fallout on them, and must be thoroughly washed. Most radioactive particles will sink, but any chance that the water has been contaminated with fallout would strongly suggest that it be filtered.