The application of multiple omics technologies in biomedical cohorts has the potential to reveal patient-level disease characteristics and individualized response to treatment. However, the scale and heterogeneous nature of multi-modal data makes integration and inference a non-trivial task. We developed a deep-learning-based framework, multi-omics variational autoencoders (MOVE), to integrate such data and applied it to a cohort of 789 people with newly diagnosed type 2 diabetes with deep multi-omics phenotyping from the DIRECT consortium. Using in silico perturbations, we identified drug-omics associations across the multi-modal datasets for the 20 most prevalent drugs given to people with type 2 diabetes with substantially higher sensitivity than univariate statistical tests. From these, we among others, identified novel associations between metformin and the gut microbiota as well as opposite molecular responses for the two statins, simvastatin and atorvastatin. We used the associations to quantify drug-drug similarities, assess the degree of polypharmacy and conclude that drug effects are distributed across the multi-omics modalities.