Monitoring activities of daily living (ADLs) for wheelchair users, particularly spinal cord injury individuals is important for understanding the rehabilitation progress, customizing treatment plans, and observing the onset of secondary health conditions. This work proposes an innovative sensory system for measuring and classifying ADLs relevant to secondary health conditions. We systematically evaluated multiple wearable sensors such as pressure distribution mats on the wheelchair seat, accelerometer data from the ear and wrists, and IMU data from the wheelchair wheels to achieve the best unobtrusive combination of sensors that successfully distinguished ADLs. Our work resulted in an XGBoost classifier with a 20-second window size and extracted features in statistical, time, frequency, and wavelet domains, with an average class-wise F1 score of 82% (with only 3 out of 12 classes being mislabeled). Our study results demonstrate that the newly investigated modality of the bottom pressure mat emerges as the most relevant information source for recognizing ADLs, while heart and respiratory rates did not provide added value for the selected set of ADLs. The proposed sensory system and methodology proved high quality in most classes and easily extendable for long-term monitoring in outpatient rehabilitation, with the need for an extended database of activities.