You already are normal. Most people have some kind of social anxiety if you dig deep enough. Just be yourself! If you want to like people as much as you want to be liked, they’ll see that. They already have or they wouldn’t be inviting you along. ^___^
Eh, I bet they hate all or most of the same things about the world and lacking a frame of reference for polite interactions as I often do, they might be wallowing in each other’s general contempt and feigned disdain.... for all I know. >___>