Teens can be moody and hormonal, but I don't think you want to write this off as a phase. He's been through a huge transition, and while this is the life of a military family, sometimes these moves occur at tough times. Sounds like that's what happened here.
He's near tears, so he's definitely upset. It sounds like you view him as a loyal friend who also has some trouble with some of his comments. He tends to be a bit narrow in his views (how things should be) but he's also been isolated because of that. It's interesting that his crowd at school said, essentially, "We didn't want to hurt your feelings so now we're telling you that we kept this secret of how you are viewed, and now you've found out about it and you're going to second-guess everything that has occurred up to this point." That's tough to hear. And it's sort of a cross between "we're trying to be good and caring friends" and "hey, we've all been discussing you." Those two things are so hard to reconcile.
One of the best ways to feel better about oneself is to be of service to others. So, 14 is a bit young for a regular summer job, and there are travel/vacation plans in place. But surely there are other things going on in the community where he could volunteer his time, be of service, achieve some confidence-boosting milestones, and meet some new people.
Some random thoughts are:
1) one-week sports camps for younger kids, perhaps at the high school - track & field, basketball, soccer - kids who will look up to your son as a role model, coaches who will help guide and compliment him.
2) vacation Bible school - help with younger kids
3) town recreation department sports or day camp programs - some sports skills perhaps, helping kids line up and keep track of their lunches, making sure no one bullies or excludes anyone, learn good vocabulary for these topics
4) animal shelter or humane society - nothing makes you feel loved like a cuddly dog or cat who needs attention
5) senior center or assisted living - help older adults with crossword puzzles, Bingo, perhaps visits from friendly pets (consider working with the animal shelter to see if there is a cooperative program that socializes the dogs and reaches the seniors), perhaps art/craft/music program assistance
6) internship at town cable TV station, running off flyers for summer programs from various departments, recycling awareness/compliance at health department, and so on.
7) Neighborhood parents' helper with younger kids who are home for the summer or only have, say, a morning camp program - take them on nature walks, supervise them in the family pool, do rainy day activities
8) vacation help for neighbors - take in mail, put out trash, water plants, walking dogs, changing cat litter boxes, etc. My son started a business doing this along with some yard work. It looked great on his college applications to have an ongoing business that expanded and that earned him the trust of various neighbors.
9) yard work - mulching, weeding, mowing
10) other volunteer agency - stack donations at food pantry, run a food collection in the neighborhood or on the base to replenish the shelves (food pantries really struggle in the summer because the demand is greater with kids at home instead of on free school breakfast/lunch programs. Turn your son into a leader by meeting a need.
All of these things make him realize others have it tougher than he does, but also that he has value and abilities that others need and appreciate.
You can do some preliminary research and let him choose, but you should put your foot down that he's not going to sit around all summer and just be by himself shooting a few hoops.
Good luck!