I don't think it's the kava. It's the attitude. It's easier said than done, but one way to get into small-talking is to pretend that you belong. Really own up on the idea that you belong where you currently are. You don't need to go full-blown "this is my domain, all bow to me." Just pretend that you aren't an outsider. Whatever kava you're drinking should put you in the correct mind-set to feel like you belong in the place you're currently at. It's stressful to think about people not liking you, whether you're at a new school, or a new job, or with relatives you don't see much. Think the opposite, like everyone likes you, because they also want to be liked and they also want to avoid being a bother. Removing the stress of concern over people finding you weird or out-of-place should make the next step below much easier.
Next step: "Who's going to break the ice?" A lot of times, especially with introverts, you have this unspoken but prevalent question and no one is willing to volunteer themself or (even more awkwardly) someone else. If you muster up some courage, you can answer that question by breaking the ice and starting a conversation. If you're not into stepping forward and introducing yourself, some structure may be useful here. Party games can really get the ball rolling. The game itself can be the conversation and perhaps you can slide into other subjects, like your old/new car, or the latest news in sportsball, or a movie you watched recently. Some kind of structured conversation like a party game is best suited for private gatherings, like at someone's house, but some public places may have giant Jenga or giant checkers. You never know without prior research or going in blind.
Socializing isn't that simple. Not everyone will like you and not everyone wants to talk, but if you're at a kava bar or even just any kind of social gathering, someone will want to reach out, take your hand, and shake. You have to start somewhere, and when you do, small-talk and BSing should come naturally with only a little practice. Don't be afraid if someone decides to initiate with you. They may be feeling just as awkward as you. Commend them on their attempt and be cordial even if you don't like their vibe.
Edit: I don't know you so I didn't want to assume that what I wrote above is something you already knew. If you already knew a particular pointer here, at least you're reminded of that little tip. If you didn't know about this, I technically did my job in putting the pieces together for you so you can be more informed with your next attempt at small talk. Sorry if it sounds like basic social skills, but I didn't want to assume anything with your scenario.