my friend...just be yourself. If you enjoying being an otaku, stay like that. Like >>7 said...you have to endure the rejection over and over again to make things better. Also (if you can) try not to play the "be someone else so I can land the girl" card. The more you act true to yourself, the more likely you will at least get an invitation or some sort...but at least try to look and act socially casual.
If you are 20, then you are still young and have a lot to experience. If you are JUST AN OTAKU...experiment on other things like sports, music (not techno/rave shit), traveling...something!!
Here's a tip: girls like guys who have an extensive portfolio of various experiences. My present girlfriend hated me before we started dating in high school. One time during Spanish class...I was paired up for an exercise with her. After we finished...I just asked her "what are your hobbies?" She said she liked to play the flute, enjoy dancing, and other things I don't remember. I responded by saying I play the violin, enjoying goin' to clubs, and played club soccer. She was so impressed that she wanted to hear more about myself.
Try it and see if it works; maybe when you are taking the bus, waiting in line at a fast food joint, or walking around the mall. Just don't look like a stalker or a creep as you approach her.