Ask a doctor. You might just have a lot of sweat glands. Stress can increase this a lot. Have you tried antiperspirant deodorant or baby powder? Also, for the smell, different soaps work on different people. Try a different soap and make sure it's a bar and not shower gel. Use a good rag not a loofah or anything similar and scrub everywhere. Also, it might be a good idea to use rubbing alcohol on your rag after the soap (not directly on genitals) and then rinse.
There are two types: Primary (focal) hyperhidrosis which only effects certain areas and is not caused by an underlying problem, and Secondary (generalized) hyperhidrosis which effects the whole body and is caused by an underlying problem.
"When the sympathetic nervous system senses overheating in the body, it sends signals through ganglia (nerve pathways) to sweat glands to produce sweat, causing body temperature to drop. Experts believe the ganglia becomes over-stimulated in primary hyperhidrosis and over-produces sweat."
I know you say you feel like you sweat all over, but really what I think is happening here (and correct me if you really do sweat all over) is that the 'heatwave' you feel throughout your body is your sympathetic nervous system over-activating itself, and the result is excessive sweating in certain parts of your body. I mean it might feel like you're sweating all over but are you actually? If it is a full-body thing then I supposedly it can *only* be caused by an underlying medical condition and strong emotions have no effect on it, but if it's only limited to certain areas (feet, armpits, face, palms of hands etc.) then strong emotions are a known cause and I guess that would be your problem, although I'm not a doctor.
Pretty sure I have a milder case of what you have though, I also feel that 'heatwave' in my body when I'm either embarrassed or highly anxious, which leads to excessive blushing (like a less severe case of Idiopathic craniofacial erythema) along with sweating in certain areas, it isn't exactly a good feeling.
Actually just adding to this...
It says on the link I posted: "Primary idiopathic hyperhidrosis - there is no apparent cause. Idiopathic means "of unknown cause". In the majority of cases the hyperhidrosis is localized."
So in other words, according to this site, it is possible to sweat all over but not have an underlying medical that causes it, although this would be quite rare. Then again I couldn't find any other site that backs this claim up...