Remember EMF discharge that will burn out the power grid—No more Power—No more computers—No internet. One bomb could send us back to the 19th Century. We all will be Amish without the cool clothes.
Honestly, I think the devastation brought by nuclear weapons themselves will prove to be overrated. Look at Hiroshima and Nagasaki today. They're flourishing. The power will come back on and many modern conveniences like cars will continue to work.
What will really cull the population will be the post-nuclear landscape. Think the whole general collapse of society. People will starve. People will freeze in the winter. Millions will die from not only radiation but various other untreated medical conditions, accidents, infections, etc. Homicides and general lawlessness will skyrocket. Many will commit suicide.
Of those who survive the blasts, it'll be the elderly and those who depend on regular medical care and prescription medicines to be the first to go. They'll drop like flies in the millions.
Young, single men without families to burden them or slow them down will fare the best. They'll take whatever they want from everyone else.