I'm an oddbod too, and can relate. I don't know why I'm odd, but I experience it as 'not fitting in'. It makes me very unhappy and I have wasted time and energy trying to 'be accepted'. Somehow it means curbing my personality, but I couldn't really say which bits...
I'm a reader and a thinker, very imaginative and like to do my own thing: I enjoy exploring the healing properties of plants, swimming in the sea in all weathers, walking by myself. I'd rather walk then drive, buy organic than standard, think that Rudolf Steiner has some interesting things to say.
There's someone locally who endlessly describes herself as the 'weird' one. If she knew how lonely it was, she wouldn't be bragging.
Also, for some obscure reason, I don't really enjoy the company of other oddbods, unless they are more accomplished or accepted than me. My closest friends are very normal, but really enjoy the quirky bits of me. I don't hide anything when I'm with them.