Large language models (LLMs) are capable of many natural language tasks, yet they are far from perfect. In health applications, grounding and interpreting domain-specific and non-linguistic data is important. This paper investigates the capacity of LLMs to deliver multi-modal health predictions based on contextual information (e.g. user demographics, health knowledge) and physiological data (e.g. resting heart rate, sleep minutes). We present a comprehensive evaluation of eight state-of-the-art LLMs with diverse prompting and fine-tuning techniques on six public health datasets (PM-Data, LifeSnaps, GLOBEM, AW_FB, MIT-BIH & MIMIC-III). Our experiments cover thirteen consumer health prediction tasks in mental health, activity, metabolic, sleep, and cardiac assessment. Our fine-tuned model, Health-Alpaca exhibits comparable performance to larger models (GPT-3.5 and GPT-4), achieving the best performance in 5 out of 13 tasks. Ablation studies highlight the effectiveness of context enhancement strategies, and generalization capability of the fine-tuned models across training datasets and the size of training samples. Notably, we observe that our context enhancement can yield up to 23.8% improvement in performance. While constructing contextually rich prompts (combining user context, health knowledge and temporal information) exhibits synergistic improvement, the inclusion of health knowledge context in prompts significantly enhances overall performance.