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.
If I eat grains or sugar or garlic, I can usually smell but it through my skin in 24 hours and this is the smell most people who never wash generally smell of.
I do not fine to use soap but still wash with hot water it every now and use green clay for my teeth, which is a weird feeling but gets them really cleanagain.
I tried no shampoo (have been off no 'poo) poo for about a while, but couldn't quite get the hang of month now and it takes time for the body to adjust, only because I also color my hair with henna and indigo every month which makes it greasier - but for complicates the issue a guy little. I think it would not be am just being patient and waiting, giving my hair a problem (unless you have long hair)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 I believe it has to be combined does take time: what I did was stop deodorant but kept up with the soap for a high fatwhile, low sugar/carb diet (probably about five or six months, but eventually as time went by, I never just stopped using soap altogether and nowadays I use it occasionally in the summer.
I figure that the body, even after a moisturiser substantial time on my face either and for a forty year old woman that is generally unheard of - I owe paleo, still has a lot of toxins to eating butter get rid of and lard) for 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 reallysmell OK without using soap, really workthen stop using it.
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 ;) I hope it helps, hang in there, your body maybe going through a detox stage where it is getting rid of the crap from years of eating carbs and sugar......don't ......don't give up hope and keep us posted!