Alright so in a one on one conversation with a girl, I'm amazing. I always end up saying the right things at the right time, I'm generally funnier, and have almost no fear of being judged. I'm unstoppable basically. But when I'm in a group of people I seem to lose all of my skill, I'm awkward, sort of boring, and I think so hard about everything I say that my chance to say it passes right by. I think I even know why. I'm assuming it's a basic stage fright reaction, but I don't know for sure. As I'm sure you can imagine, this completely wrecks my usual game. Either way my question is: How do I get over it?

Inner game. You are the man, remember? You don't need to over think the stuff you say, you know it's going to be funny, you know it's going to be interesting.

When you are the centre of attention in a group of people women will pick up on that. In fact they are impressed by your confidence to command a group of people and be completely unafraid. If you approach a group of people you don't even know and can instantly get their attention then you are DHVing like a motherfucker. Especially if there are other guys in the group, you just out alpha the shit out of everyone like that.

Damn, I have the exact same kind of problem!
May I ask you something: Did you grew up with sisters?
Anyway, something that helped me a bit:
-Speak LOUD AND CLEAR!
-Allways have a tease in your eyes - combined with your clear voice, people will laugh no matter if you say something boring, because they will think you dont mean it and just makes fun of the obvious answer (obvious is often related to boring).

I'm a simple guy with a simple way of thinking. I don't have the best and creative answers to a convo in a group, but when I think of something fun to answer, I try to be as serious as I can and just say it - this will boost the fun.
In groups (4+, all males or mixed) the convo will either be about something funny/joking, opinion-talking or stories.

Funny/joking:
A hard one, because you have to think fast.
This is where it's good to use the "tease-expression", if you only think about something boring to participate with.

Opinion-talking:
The easiest one, and if I guess right, this is where you are most relaxed in the convo with groups. Just make up your mind as fast as possible about what opinion you have on the subject and say it. It dosen't matter if it's a cliché thought, just keep it simple, and someone will eventually build further on what you are saying. This can get you in a very talk-active mode, because when you say your opinion and it is out in the ocean, you'll have to stand by it and not be distracted by other thoughts in your head.
[This is where it's also good to use the "tease-expression" if you want to be a bit cocky/flippant/provocative]

Stories:
Prepare and train some good and fun stories before socializing. Keep in mind that when you tell stories it have a much better effect when you slow down your talking-speed and really build up the story to a climax. Learn from the internet. Try to google:
"How to be good at telling stories".
Observe things that happends when you are alone in the public and overdo the scene when you tell the story.

Important:
Don't take yourself too serious when in groups. Have dignity, but making fun of yourself can be a good way of socializing in groups. Just only do it with your small flaws.
Like telling a story where you were out clubbing with your girlfriend and had to go to the bathroom. When you came back you accidently grabbed a wrong girl's hand because you thought she was your girlfriend.

Girls often discuss serious things in groups, but it seems like you are more relaxed around girls, so I guess talking and being funny in female-group won't be a problem for you.

I hope my advice helped you - it have worked for me, but it isn't something that are "approved" by the Professional PUA's.
Would like to hear some opinions about my thoughts from other people in this forum.