In my own personal experience, going paleo meant smelling sweeter - after about a month on the diet, my breath smelled loads better (I lost the white coating on my tongue) and body odor was nearly non-existent after about 6 months. I agree with Ed, if I start using soap a lot, then my sweat glands seem to compensate somehow and start to work overtime again, but it is fine to use it every now and again.
I have been off no 'poo for about a month now and it takes time for the body to adjust, I also color my hair with henna and indigo which complicates the issue a little. I am just being patient and waiting, giving my hair a little soap at times when it needs it, just washing in water if it is OK with that.
And the no soap thing really works, but it does take time: what I did was stop deodorant but kept up with the soap for a while, probably about five or six months, but eventually as time went by, I just stopped using soap altogether and nowadays I use it occasionally in the summer.
I figure that the body, even after a substantial time on paleo, still has a lot of toxins to get rid of and this is probably what you are smelling on your skin right now. Just give it time and take it in stages; if you smell OK without deodorant then stop using it, if you then start to smell OK without using soap, then stop using it.
I have a vision of Paleo man as genteel, smelling sweet and having just enough of the right BO in the right places to attract a paleo gal ;) I believe Paleo girl smelled sweet but her odor changed throughout the month (which is what I notice) in order that paleo man need not have to second guess her ;), this could have also been a great way for paleo gal to keep on top of her own fertility/reproduction cycle.
Some sweat is definitely a good thing for successful male/female interaction and eating paleo style means, after a while, sweet sweat, which is even better for successful male/female interaction. I think it also depends on how much hair there is around to keep that odor trapped next to the body and what use that can have when things get personal.
This is my own experience of course, my husband has not complained yet ;) ......don't give up hope and keep us posted!
Here is another good account of no soap, no 'poo