Sorry to hear about your problem. The only thing I will say is that you are lucky your family can semll it and have told you it exists. Many people with different types of body odour cannot smell it and close family members cannot either, so they keep getting told they are mad!
You do not say if it is a sweaty type of odour or some other odour? Before you noticed you had an odour did you by any chance have to take Antibiotics , steroids, contraceptives? The reason I ask is that sometimes after taking these types of pills you can create a bacterial imbalance in your gut by killing off too many good bacteria, so you can develop candida and or bacterial overgrowth.
From your diet it does not sound like you take many carbs, so candida may not be the problem. There is a condition called fructose malabsorption and some people can develop milk cases of this, and it can apparently cause the body to give off smells like rotten fruit?
You could perhaps get some tests done to establish the condition of your intesines - blood, urine and stool tests may give an indication if there is a bacertial problem or a parasite? Some people have got help from a Chinese herbablist, so this is another possible method to try to source the underlying issue. Apparently rhubarb root and ginger root are good for the intestines and one girl claims they helped her to eliminate her odour.
Also, have you tried taking digestive enzymes with food. Sometimes the body does not work as well as it should and taking digestive enzymes can help. Also Charcoal tablets help to absorb any internal gas/odour, and also copper chloophyllin works as an internal deodorant - you can take them together.
Some people take zinc, and or magnesium - read up on these.
You could also try some good probiotics. You could try taking the enzymes, charcoal, chlorphyllin and probiotics tgether, or start to take them individually and see if you get any results.
Although your diet might be good, you could be allergic to some things in your diet - why don't you try an elimination method - start to take certain items out of your diet and see if there is any improvement.