How can I stop being so tense and uncomfortable from a friend group where I feel betrayed?

MP, thank you very much for asking your question.  It sounds like that you may be better off from not being involved with this friend group.  When answering these questions I am doing so without the benefit of asking you questions for clarification or further information.  This means that I have to make some assumptions. Have you spoken to them about this?  It's possible they have mis-interpreted some of your cues, and vice versa.  You could ask to meet with them and during that time you would state your observations in a very neutral, factual statement.  "I've noticed that I have not been invited to xyz."  or "I've noticed that I am the only one that plans events, and when I don't, I'm not invited."  Then, you would state how that makes you feel.  "I feel left out in spite of the times I have included you all in my plans."  That's just the start and I would only suggest having this conversation if you would like to reconcile the relationships, or if you feel compelled to get it off your chest.  Resist the temptation to say the actual word, "why?"  This tends to put people on the defensive, and, since, it's multiple people, it would feel horrible to you to have them gang up on you.  

Now, if you plan to not have that conversation, and you are pretty sure that you have ended these relationships, let's talk about how you can move on and feel better.  One confusion I have about your question is that I'm not sure you are feeling tension ABOUT this situation, or if the others are imposing some discomfort and tension ON you.  The latter situation, you cannot do much about.  I wish there was a way to "make" others do things, but there is not.  You can ask them to stop doing whatever, or stop blaming you, but there's absolutely no guarantee to keep them from doing that.  If they are blaming you for the distancing, how do you know that?  Did they say it to you, or did it come via a rumor?  Or, did you make that assumption?  If you hear it from them, this is an opportunity to have the previous stated conversation.  If it's a rumor (or from the grapevine, or mutual friend), you do not even have to address it.  How would that look?  A mutual friend comes to you and says, "I've heard you are no longer friends with xyz.  What happened?"  You can respond with something like, "We all just kind of grew apart."  Now if that's a close friend, that may be an opportunity to vent.  But, theres not a lot of value long term in indulging those who bring rumors to you.  Yeah, I know, this is an opportunity to sling back your own rumors, or get even, or clear the air, but it rarely does and just keeps the drama stirring.  

Now, the real meat of the question - how do you move on?  One big thing is to not indulge yourself in revenge fantasies.  These may be as simple as fantasizing what you would do or say if xyz happens.  Instead, recognize that you are doing that, get up and do something different, like plan things for yourself to go out and do solo.  You may not feel like it at first, but it's an exercise of the healing part of moving on.  Start the task of developing new friendships.  Do some gratitude work.  That can look like: being grateful for the lessons you learned from being in that friend group, being grateful that you now have more time and opportunity to develop new, and, possibly better relationships.  Then, at some point, you can release that resentment and forgive them, not because they deserve forgiveness, but because, you deserve peace.  

I hope this was helpful.  If this feeling continues on for too long, it may be a thought to consider therapy, especially if it interrupts work, ability to enjoy life, or interferes with other relationships.