Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators offer much faster inference. Their ability to integrate volumetric imaging with scalar metadata remains underexplored for biomechanical predictions. Objective: This study evaluates multimodal neural operator architectures for brain biomechanics. We test strategies fusing volumetric anatomical imaging, demographic features, and acquisition parameters to predict full-field brain displacement from MRE data. Methods: We framed TBI modeling as a multimodal operator learning problem. Two fusion strategies were tested. Field projection was applied for Fourier Neural Operator (FNO) architectures. Branch decomposition was used for Deep Operator Networks (DeepONet). Four models (FNO, Factorized FNO, Multi-Grid FNO, DeepONet) were evaluated on 249 in vivo MRE datasets across frequencies from 20 to 90 Hz. Results: DeepONet achieved the highest accuracy on real displacement fields (MSE = 0.0039, 90.0% accuracy) with the fastest inference (3.83 it/s) and fewest parameters (2.09M). MG-FNO performed best on imaginary fields (MSE = 0.0058, 88.3% accuracy) requiring the lowest GPU memory among FNO variants (7.12 GB). No single architecture dominated all criteria. This reveals distinct trade-offs between accuracy, spatial fidelity, and computational cost. Conclusion: Neural operators augmented with multimodal fusion can accurately predict full-field brain displacement from heterogeneous inputs. They offer inference times orders of magnitude faster than finite element solvers. This comparison provides guidance for selecting operator learning approaches in biomedical settings.