Sleep apnea (SA) is a common sleep disorder. Identifying patients at risk by means of comprehensive monitoring that requires overnight stay at professional sleep clinics are costly and inconvenient and can lead to unreliable results in view of the unfamiliar sleep environment. Existing wearable devices for sleep monitoring, which can be used in a familiar home environment, do not provide the same comprehensive monitoring as through clinical monitoring. The larger objective of the present work is to develop a sleep monitoring system for home use, which can provide comprehensive monitoring. In the development in this paper, machine learning (ML) models are explored for the classification of SA and sleep stages using multisensory data, without neglecting any of the required signals. The data acquired through the sensors are normalized, their features are extracted using Composite Multiscale Sample Entropy (CMSE) and are standardized using a robust scaling algorithm. Processed features are classified using a Neural Network (NN) and the obtained results for the SA classification are compared with those obtained by using a Support Vector Machine (SVM) approach. The impact of neglecting signals when classifying sleep stages is analyzed as well. The results are presented in the paper and observations are made. The NN model trained with the Bayesian regularization algorithm has provided an overall average accuracy of 94.5% and performed slightly better than when trained using the scaled conjugate gradient backpropagation algorithm (93.2%). The SVMs have yielded lower accuracy levels compared to the NNs (<92%). It is observed that the use of all 14 signals for SS classification yields an overall test accuracy of 72.3%, which is higher than that when one or few signals are used. It is concluded that ML models are effective in classifying sleep data from multiple sensors. Accuracy levels are higher when fused multisensory data are used as inputs. Furthermore, NN models are found to be better suitable in practical application and can be incorporated into an inexpensive and convenient wearable device that can carry out comprehensive monitoring.