Looking for ideas to help my sixteen year old Son

I have a sixteen year old Son, who over the years has seen the Paediatrician on and off, with a view to having a formal ASD assessment in conjunction with school. 

This has never happened and in the end I gave up. Official diagnosis or no official diagnosis, he clearly presents with some milder Asperger's traits and as he moves into young adulthood, life is getting trickier for him. 

I feel that his difficulties are a hidden barrier to his development as a young person, because his traits are not always obvious to others.

He is painfully shy and awkward in social situations, particularly at school, to the point that it gives him anxiety.  He often says he feels physically unable to speak if he is asked a question in class, for fear of his peers mocking him. I think this is because he has a reputation for being a quiet loner and a bit quirky. He certainly has difficulty making 'small talk' type conversations. He just doesn't get that for the most part. Everything is an intensely academic and philosophical discussion with him, bordering on a lecture

His way of dealing with this over the past few years has been to keep his head down and make himself as invisible as possible.  He does have one friend in the year below him at school that he hangs out with at lunchtime, but I wouldn't say they were close. 

He also never goes out in the school holidays, unless it's with family members.  So he isn't learning to be independent, which is a worry. 

Lately he has expressed his frustrations to me about how he wishes he could fit in. He feels like no one gets him amongst his peers and his differences have become more apparent to him as he enters young adulthood.  He uses words like outcast and weird to describe himself.

I want to find him some ways to start socialising with other people his age, that experience similar difficulties socially, but I don't really know where to start. 

Apologies for the big speech. I've never used a forum before and have never really talked about my Son's issues to anyone other than close friends and family before. 

But if anyone on here has any advice,  it would be most welcome.

Thanks.