We propose a system that estimates people's body and head orientations using low-resolution point cloud data from two LiDAR sensors. Our models make accurate estimations in real-world conversation settings where the subject moves naturally with varying head and body poses. The body orientation estimation model uses ellipse fitting while the head orientation estimation model is a pipeline of geometric feature extraction and an ensemble of neural network regressors. Compared with other body and head orientation estimation systems using RGB cameras, our proposed system uses LiDAR sensors to preserve user privacy, while achieving comparable accuracy. Unlike other body/head orientation estimation systems, our sensors do not require a specified placement in front of the subject. Our models achieve a mean absolute estimation error of 5.2 degrees for body orientation and 13.7 degrees for head orientation. We use our models to quantify behavioral differences between neurotypical and autistic individuals in triadic conversations. Tests of significance show that people with autism spectrum disorder display significantly different behavior compared to neurotypical individuals in terms of distributing attention between participants in a conversation, suggesting that the approach could be a component of a behavioral analysis or coaching system.