English as a Second Language (ESL) speakers often struggle to engage in group discussions due to language barriers. While moderators can facilitate participation, few studies assess conversational engagement and evaluate moderation effectiveness. To address this gap, we develop a dataset comprising 17 sessions from an online ESL conversation club, which includes both moderated and non-moderated discussions. We then introduce an approach that integrates automatic ESL dialogue assessment and a framework that categorizes moderation strategies. Our findings indicate that moderators help improve the flow of topics and start/end a conversation. Interestingly, we find active acknowledgement and encouragement to be the most effective moderation strategy, while excessive information and opinion sharing by moderators has a negative impact. Ultimately, our study paves the way for analyzing ESL group discussions and the role of moderators in non-native conversation settings.