Effects of Radiation
It's a common misconception that radiation poisoning and nuclear fallout would be the source of the majority of fatalities resulting from a nuclear attack. This isn't the case: most deaths would result immediately from the force of the blast itself (but not the blast—we'll get into that). If you were to detonate every weapon constructed during the Cold War, the resulting exposure would be well below doses lethal to humans.
Most Powerful Weapon
The Russian-built Tsar Bomba stands as the most powerful weapon ever made, nuclear or otherwise, with a yield of 50 megaton TNT. This is more than twice as powerful as the strongest American weapon. The Tsar Bomba destroyed all buildings in Severny village some thirty miles away. Only one bomb of this type was ever made.
It Isn't Always the Blast, It's the Blasted
Distance determines if the force of the blast itself will kill, but a bigger threat is the destruction of structures and the launching of objects through the air. Depending on the yield (between twenty kilotons and twenty megatons), a concrete building anywhere from half a mile to five miles away from the blast. And any objects not obliterated potentially become deadly projectiles.
This isn't a matter of whether or not nuclear weapons still hold a strategic advantage—that's a whole 'nother kettle of fish—but rather the stockpiles themselves, in America at least: the oldest warheads are over twenty-five years old and many of the buildings used to store them twice as old. The kicker, though, was revealed in a news piece in 2014: records related to stockpiles were kept on eight-inch floppy disks. Recently the United States has put into a motion a plan to modernize its nuclear arsenal.