What makes them so strong and deadly?

Blast Wave

The blast wave is the immediate destruction from the bomb. Extreme levels of heat from the fireball, causes a high pressure wave to form. The wave then moves outward producing the "Blast Effect". The very front of the blast wave, which is called the shock front, travels at high speed away from the fireball as if it is a moving wall. The air behind the shock front accelerates immediately causing very high pressures and a strong wind. The strong winds then create dynamic pressure against the objects that are facing the blast.
Shockwave of Atomic Bomb Impact!! Must see! (Trinity and Beyond)

Blast wave effects on humans

Humans can actually resist most blast waves that are under 40 psi (pounds per square inch). The lethal part of a blast wave is the buildings that it knocks over. More humans would die from the effects on buildings from the blast wave than the blast wave hitting themselves.

Radiation effects on parts of the body

Hair -- Losing hair very rapidly and in clumps happens at 200 rems or higher

Brain -- The brain will not be damaged unless the radiation is 5,000 rems or higher. This could result in seizures or immediate death.

Thyroid -- In plentiful amounts, radioactive iodine can destroy parts of the thyroid or all of it

Blood system -- If the person is exposed to 100 rems the blood's lymphocyte count will decrease. This would make the victim much more susceptible to infection.

Heart -- At 1,000-5,000 rems of radioactivity would immediately damage blood vessels and could cause heart failure or death

Hiroshima Nuclear bomb effects

The death toll was estimated to be around 130,000. Over 90% of people within 500 meters of ground zero (where the bomb was dropped) died. At about 1 mile 1/3 of people died and the other 2/3 had injuries. Then at 2 kilometers 50% of people suffered injuries and 10% died. 1/3 of the total deaths happened in the first 4 days, and 2/3 died by the 10th day, and 90% of people died after 3 weeks. Injury rates were higher than death rates in the city. Everything in the city within 1 mile of the blast was destroyed except for a small amount of buildings, about fifty. The fifty that stood standing had been whipped out of all of the insides of the building including windows.