I think it's a matter of not focusing so much on how you're performing, but on the other person. Shift your focus towards the way their mouth moves when they speak, where they place their hands, their eyes, etc. Eventually you'll realize that the fact that you're worrying so much is what's actually going to make you seem 'awkward', because you're focusing on the wrong things. Simply talk to other people the same way you'd like them to talk to you, by being pleasant, nice, and interested in what they're saying.