Energy release by the bomb probably isn't the right metric here. A multimegaton bomb spends a lot of that energy heating plasma into hotter plasma. This has minimal climate impact.
The scenario the nuclear winter researchers had in mind was that those 100 bombs each start catastrophic fires that burn down major cities. Those fires can produce lots of soot and ash that have climactic effects, and then lift the particulates into the stratosphere.
I don't have enough of a background to comment on whether and why those fires would be worse than a large brushfire or forest fire, but I'm pretty sure it isn't about megajoules of energy.
If it isn't about MJ, then it is about the amount of dust and soot?
Pinatubo ejected about 10 cubic kilometers of dust into high altitudes. The potential energy of this dust was far greater than the energy of all atom bombs. Ignite them all and you will get just enough energy to get 1 cubic kilometer of rocks a few kilometers high.
It was no nuclear winter, again, from Pinatubo.
Just a reminder that some of the old threats are still around (and hence that AI is not only something that can go hideously badly, but also some thing that could help us with the other existential risks as well):
http://blog.practicalethics.ox.ac.uk/2012/03/old-threats-never-die-they-fade-away-from-our-minds-nuclear-winter/
EDIT: as should have been made clear in that post (but wasn't!), the existential risks doesn't come from the full fledged nuclear winter directly, but from the collapse of human society and fragmentation of the species into small, vulnerable subgroups, with no guarantee that they'd survive or ever climb back to a technological society.