Sorry this is so long but your post obviously resonated with me. Your son sounds like ours when he was that age. I used to worry about the same things. Was he going to be a lonely person in his life?
Our son used to have a really small group of friends, with one or two he would call his best friends. I signed him up for sports (soccer, baseball, swimming) but none of them were really his thing. We also tried a children's chorus and piano lessons, but those weren't his thing either. He loved a children's theater, which was two weeks each summer, but he has aged out of that at this point.
Our son has always been on the older side of classmates, having missed the cut off for the next higher grade by just ten days. Even so, he tended to be on the less mature side and was often sensitive to social slights or a little clueless socially. He usually just had 1-2 main friends he spent time with.
I often was the instigator of play dates. I also worked hard to encourage our son to make the calls himself to get him comfortable doing that. But it often felt like we were the inviters...rarely the invitees.
Fast forward to today...our son will be 14 in October. He is often the friend organizing get-togethers. (He had a fun sleepover, inviting six friends, on the last day of school which he had planned for months.) He's got a core group of 4-6 friends that he spends time with, ranging from 1 to 4 at a time, and they reciprocate with calls as well.
It was time well spent to teach him to initiate those calls. He is now pretty comfortable doing that. He still is apprehensive, at times, if he thinks the friend will not be available. But in general, he has blossomed in the friends department.
The important thing to remember is not the quantity of friends but the quality of them. But it's also important to realize that one friend can rarely meet all one's needs. It took our son time to realize the latter lesson. He tended to wear his friends out. As we taught him that one friend can feed one part of him while another can feed another side of him, he learned to broaden his circle of friends. It has taken time and some parental coaching on occasion, but it has been wonderful to see his circle widen through the years. It was too hard on him and his friends when he expected one child to meet ALL his needs.
As for birthdays, after the age of ten, we began having birthday parties that were very small. We encouraged him to invite 1-2 friends and we went somewhere special--rollerskating, the Boston Museum of Science, etc. Doing this allowed the day to be a fun trip somewhere, along with some good one-on-one time for him and his friend(s).
Get this...now we've decided that he can invite a bigger group at home again, if he wants to, because "he doesn't want to leave anyone out". So, next year, I think we'll be back to having his birthday parties at our house with multiple friends. Whodathunk?!
Our son is a complex child. I usually describe him as a delight and a challenge. He is an only child. He is bright but doesn't always use it in school. He tends toward the low end of ADD which gets in the way at school or with friends on occasion. He's got a delightful insight into the world, a dry wit, an incredibly logical mind, and a wonderful singing voice. He loves his stuffed animals, Legos, video games, Nerf dart paraphernalia, and spending time with friends. While most of his pals have moved beyond some of these things, like stuffed animals, he still maintains a close bond with them.
I have come to trust that he is developing at his own pace and that is a good thing. I still wonder what niche will be his thing, but he has gained some confidence throughout the years. One of his best friends just moved away so I find myself wondering how that will affect him. But he has a good group of friends who are still in the area and he said he actually wants to go out for the soccer team this coming year in 8th grade. Huh? Fine with me!
It's still a challenge sometimes to get our son to move beyond his comfort zone. But we try to be gentle in our nudging, trying to get him to do his own nudging as the years progress. Ironically, as opposed to the prior two summers, I actually insisted that he sign up for swimming again this summer (the only sport that can potentially save a person's life) and one additional activity.
Mainly, this insistence is to make sure he doesn't bury himself in a non-active summer of TV or videos. He is usually good about getting his friends to turn off the games and to go outside for some fun running around. But I want to make sure this trend continues. He and his friends are all changing at different paces, and I'm working a little more this summer, so I want to make sure there are a couple outlets in his days to help expand his horizons. Of course, I'm "ruining his summer" but he usually likes the activities once they begin.
So, have faith, and trust your intuition. When you think you need to coach your son in one skill or another, go ahead and forge forth. But also trust that time and life will teach him important lessons as he moves along in life.
Good luck and enjoy!