CleanaholicSpendaholic I am really sorry this sounds crap.
I would start looking for another job and I would most DEFINITELY NOT think that it was any kind of failure! I would make sure my boss knew exactly why I was leaving too.
But before it gets to that I would (I am afraid I would want to because I am a bit bolshy!) try inserting myself into their shenanigams and see where it got me. Please only do this if you feel strong enough for rejection but if you were looking for another job it may not be so hard to bear knowing you are leaving, and if it gets better before you leave you could always stay! 
Examples would be....
As people are heading out to lunch just ask if you can join them. The may say no which is really rude and unpleasant and I would note that down to tell the boss. YES people can eat with whomever they want, of course, and if it were just a small group of two or three I would respect their privacy and they may be discussing someone's operation or baby or private matter, but a whole gang of them they should welcome you. Because work is work and a lunch break is just that, not some major social exploit, IMHO!
I would ask the Secret Santa organiser who you were getting for Secret Santa, but do be aware if they are super determined to be mean they might get you to buy for someone else and not buy for you (note that to tell boss when you leave). If they are going to be shitty they should be called out on it!
Lastly, if someone is leaving, stride into the office and ask where 'Gillian/Ben/Toby/Beatrice's card has got to as you have not signed it yet.
All these things do require a degree of gumption and in your shoes I may well not have the gumption to do it! But this is what I would like to do!
If this all seems too much, pick the nicest, pleasantest of the office gang and speak to her/him privately about these issues in a friendly manor - not 'why aren't I invited - but I'd like to join you all for lunch next time you go, and just see what they say.
Also, if there are other members of the office who are not in the gang, why not befriend them.
Let us know how it goes.
Good luck.
jemimavintage hugs to your, those work colleagues from 25 years ago sound crap.