I would actually recommend dropping this line of questioning. It's perfectionist. And treating it as a problem that needs to be solved (in effect treating you as a problem to be solved) just puts extra scrutiny/attention/pressure on it that will make it worse. It's just a habit that you will grow out of naturally with more experience around people. And that will happen faster if you forgive yourself, accept yourself as you are, and accept each situation as it is and each person as they are. A lot of situations are inherently awkward, will be less than perfect, and will bear no resemblance to the snappy scripted dialog in TV/movies. Wishing things were different from how they are, is 9 times out of 10 where the problem itself comes from - in your case being in an awkward situation, and being hyper-aware that it's awkward. Younger children are awkward but don't know it, and most of them seem happy enough. Forget about it. Everybody is at some level of gracefulness. Is everybody "awkward" who isn't perfect? Even Olympic figure skaters probably stub their toes on their coffee-table legs.
The other thing to realize is that the awkwardness is an inward-looking and (to apply a sort of judgmental slant on it) ultimately kind of self-indulgent habit. People around you are probably just as nervous and awkward as you, and seeking signs that it's okay and safe to be themselves. What signals are you giving them? You could be a leader to them, showing them the way. Be curious about them, reach out and ask them how they're doing, take an interest in them and what they have to say. That's the best way to forget about you, i.e. literally lose your self-consciousness. If nothing else it will at least take the spotlight off of you for a few seconds while they talk, which might be a relief. But people really appreciate when you take an interest in them, and they also appreciate (this will sound a touch cynical) the opportunity to talk about themselves. You will be well-liked. Although in the long run just don't give too much slack to people who latch onto you as a "good listener" and never give you a chance to talk! They should be willing to let you talk sometimes. And by the same token you should be ready and willing to share about yourself, not just asking questions about others like an interrogator. But in general, start with asking about and caring about others; that's the foundation of every meaningful relationship anyway.
Disagree with the first graf, totally agree with the second! I sort of like your point about just not worrying about it. But I found that I could improve my self-confidence by working at it, and it was ultimately worth literally millions of dollars and much more happiness to me. Also meant that I was always able to meet wonderful romantic partners and I am… not good looking at all.
The other thing to realize is that the awkwardness is an inward-looking and (to apply a sort of judgmental slant on it) ultimately kind of self-indulgent habit. People around you are probably just as nervous and awkward as you, and seeking signs that it's okay and safe to be themselves. What signals are you giving them? You could be a leader to them, showing them the way. Be curious about them, reach out and ask them how they're doing, take an interest in them and what they have to say. That's the best way to forget about you, i.e. literally lose your self-consciousness. If nothing else it will at least take the spotlight off of you for a few seconds while they talk, which might be a relief. But people really appreciate when you take an interest in them, and they also appreciate (this will sound a touch cynical) the opportunity to talk about themselves. You will be well-liked. Although in the long run just don't give too much slack to people who latch onto you as a "good listener" and never give you a chance to talk! They should be willing to let you talk sometimes. And by the same token you should be ready and willing to share about yourself, not just asking questions about others like an interrogator. But in general, start with asking about and caring about others; that's the foundation of every meaningful relationship anyway.