Regarding body odor, see previous threads: http://paleohacks.com/questions/3042/lemon-juice-as-a-deodorant and http://paleohacks.com/questions/1484/how-did-grok-deal-with-bo .
RE quantity of sweat, excessive sweating is called hyperhidrosis. It can occur either in eccrine or apocrine (armpits and groin) sweat glands ( http://www.mayoclinic.com/health/sweating-and-body-odor/DS00305/DSECTION=causes ). Your sweat glands are connected to your sympathetic nervous system. This means that anything that stresses you out will increase sweat output. Conversely, I would expect a relaxed, paleo lifestyle to actually decrease sweating, except during intense exercise.
Botox is one approach to excessive sweating, but it wears off after about 4 months and treatment must be repeated to be effective.
The most effective antiperspirant I've seen is a prescription agent called Drysol. Quoting myself from a previous post: "Anti-perspirants do not work on the surface of your skin. They actually penetrate the sweat glands, which takes several hours. The best time to apply anti-perspirants is at bedtime. If you shower the next morning, the anti-perspirant will still work because it's inside your sweat glands, not on the surface. A good resource for those with hyperhidrosis is the Hyperhidrosis Society ( http://www.sweathelp.org )."