Clinical decision-making in oncology involves multimodal data such as radiology scans, molecular profiling, histopathology slides, and clinical factors. Despite the importance of these modalities individually, no deep learning framework to date has combined them all to predict patient prognosis. Here, we predict the overall survival (OS) of glioma patients from diverse multimodal data with a Deep Orthogonal Fusion (DOF) model. The model learns to combine information from multiparametric MRI exams, biopsy-based modalities (such as H&E slide images and/or DNA sequencing), and clinical variables into a comprehensive multimodal risk score. The model learns to combine embeddings from each modality via attention-gated tensor fusion. To maximize the information gleaned from each modality, we introduce a multimodal orthogonalization (MMO) loss term that increases model performance by incentivizing constituent embeddings to be more complementary. DOF predicts OS in glioma patients with a median C-index of 0.788 ± 0.067, significantly outperforming (p=0.023) the best performing unimodal model with a median C-index of 0.718 ± 0.064. The prognostic model significantly stratifies glioma patients by OS within clinical subsets, adding further granularity to prognostic clinical grading and molecular subtyping.