They are, obviously, quite close in meaning and there are certainly many cases where you can use both of them.
Meiden means that you try to avoid someone or something. Vermeiden means that you try not to do something or that you act so that something won't happen.
So, the similarity and their overlap is quite obvious. For example, if I try not to look into your eyes, I can use both. Both definitions can be applied: I try to act so that an eye contact won't happen, and I try to avoid eye contact.
That makes it hard, to tell which word to use in these cases. Native speaker might have a tendency to one over the other with certain collocation. With reference to the eye contact example, vermeiden is way more common.
That said, actually you just need to think of which definition you can apply and if one of those is not possible, you certainly go with the other one.
In your second example, you can use both words meiden and vermeiden. Meiden is much more common but I heard vermeiden there quite a lot, too.
Actually, now that I read other answers, I agree that meiden is here the general rule (so I try to avoid the traffic everyday) and vermeiden is rather associated with my current situation (so I try to avoid the traffic right now).
This can be applied to other examples as well.
Your first example, however, is somewhat ... odd. Kohlenhydrate is nothing I would meiden or vermeiden. I'd rather say something like:
Ich vermeide es, zuviele Kohlenhydrate zu mir zu nehmen.
Actually, when ever you start a sentence like that (i.e. using the expletive es), you use vermeiden. There are some hits on Google for "Ich meide es", but they're all quite weird.