Alcohol.
Hell, it did for me! (As in, me being very drunk, not her! All the time.) I didn't try any pick-up stuff, I just swanned around being my drunken self and it would appear that the other half found me quite endearing.
FoxEye -- I have exactly the same social issues as you. I don't like new groups and I find it exceptionally difficult to engage in conversation with new people (and even friends, a lot of the time). My brain just stonewalls. I can't think of a single thing to say or discuss unless it's about a specific topic that I have in-depth knowledge or appreciation of. Then I just start rambling about crap that they have no interest in. So I just don't talk. Seems the better option to me.
I also have the same problem with eye contact. I've been practicing for years and gotten a little further, but still can't maintain it for more than a few seconds. It feels DEEPLY uncomfortable. Almost threatening, in a way.
So, a lot of the time down the pub I just end up cradling my drink and staring at the floor or table. I know it's not right in terms of being in a social situation. In my own little bubble I'm fine there with my thoughts, just having a drink and drifting along inside my own head, but others think I'm upset or moody or something.
Around new people I tend to be extremely offensive, but that's just my sense of humour. Due to that I usually "click" REALLY well with certain people, but go down in flames with others within minutes. Just the way I am.
So I'm very similar to yourself in terms of that, except I justifiably loathe the ugly fat piece of crap that I actually am. I put on a massive amount of weight over the course of about 4 years and it's destroyed me both physically and in terms of self esteem. I don't like looking in mirrors and, hell, I barely even enjoy going outside. But I'm working on it. Lost about 2 and a half stone, but still have around 4 to go.
Of course, after that I'll have to deal with the extra skin etc. that'll no doubt be left, so I'm left wondering whether I'll EVER be truly happy with who I am. Believe me, you're a decent looking bloke and certainly not fat.
If you lived anywhere near me I'd take you out for a drink (no homo). Perhaps our combined awkwardness could cause some kind of dimensional rift.