I don't mean electroconvulsis "therapy" like in the old days of cooping up people with psychiatric conditions...heh...but rather, pushing the envelope or continually shocking your comfort zone, as it were, to the point where your social awkwardness noticeably diminishes.
Like if you set yourself a target to talk to say 100 strangers in a month, just start a conversation about anything, observe their reactions, go to a mall or someplace to do this...and see results. To be more challenging, speak with people of the opposite gender more often.
Think of it like an analogy of shocking your muscles as you go to the gym, and progressively lift more weight.
I think this is the challenge we face(d), for so long, we've been stigmatized and excluded from interacting with others like in a controlled setting i.e. school, and didn't garner the experience we needed - so that contributes to a large degree to our awkwardness. We end up with a lower station in life on the average and that drastically impacts confidence and projects awkwardness, b/c we approach interactions as if "this person's life is probably great, and meanwhile mine's passed me by." Whereas you compare us with dyslexics, who have also had a rough go in life - but they at least didn't need the book's permission to interact with it, while we required people our age to want to interact with us to build that experience. So dyslexics can still turn out more confident later on. What this means is, we have to keep practicing, more so in an uncontrolled environment where most people don't know each other and can't collectively ostracize us, so that we can follow a similar trajectory as the dyslexic (i.e. tackle it early on in life too!)
However, some devils advocates may point out that we've been walking for a long, long time w/o anyone posing obstacles to us doing so, but we still may be seen as "walking awkwardly" when we wouldn't intuitively know the difference. So, I dunno - arguments on both sides.