I'm really sorry for what you've been through. It must be hell. I agree with a lot of advice here, and would like to recommend reading Toxic Parents (which helped me think of all relationships differently, not just parent-child), which is available as a free PDF on some websites. I also recommend The Angry Therapist, who runs a blog among other things, and promotes the lifestyle and mentality that I found the most helpful.
I wish I could give more specific recommendations, because over the last two years, I've read countless articles and made even more personal notes in something I call The Feel-Good Book. In it, I write self-help strategies, make lists of what I'm grateful for, doodle, and otherwise devote that space to non-negative thinking. I don't use it as much now, only for my daily gratitude section, since it's become a reflex now to be more balanced.
I was homeschooled. Up to a point, I did go to groups and I had friends (who all hung out with me because of my cooler older sister, but that's another story). After I turned twelve, my parents stopped trying. I saw people sometimes, but it all dwindled away, especially when I moved across the province. I nicknamed this place Exile. It is the most beautiful place I've lived, but it is also riddled with painful memories. For years, I considered myself to just not be that social; it's only recently that I've discovered just how much connection I need, which seems contrary to my introversion. When I lived in Exile, I only left the house once or twice a week with my parents, and just to run errands with them. I went 7 years with little to no socialization.
I also began experiencing anxiety there, and when that became too much, I gained severe dissociation for three very long, dark years. I've also had depression on and off since I was twelve, and that hit me hard, too.
Almost three years ago, I moved again and got my first job at the ripe age of 20. It's only in the last six months that I've started to understand socialization better. I had kept trying different tactics with co-workers, to no avail. I felt terrible that the people around me were getting along and were friends, but I just couldn't seem to get the hang of it. I thought something was missing; I thought I wasn't good enough, I thought nobody liked me. But I was determined to figure it out.
The answer was this: these people had the willingness to try. They were willing to have friends, they were willing to put themselves out there, they were willing to be rejected. They were willing to look stupid, too. And you know what I realized? The unwillingness to try, or shyness, is only a variety of fear, and fear was not something I wanted holding me back. So I became willing. Every time I was afraid, I laughed instead of cried, and I did it anyway, and it was great. Another thing I learned is that procrastination was taking over my life, in spite of how much progress I'd made; as it turns out, it's only the first step in most things that is the hardest, and the ones after usually don't need the same motivation.
Social skills are definitely something I think everyone needs to have, and I know it's important to you. Do what you can with that, but focus on how you feel about yourself first. A big part of being social means believing that you deserve to be heard. You're worthy. You matter.