Neural implicit representations have had a significant impact on simultaneous localization and mapping (SLAM) by enabling robots to build continuous, differentiable, and high-fidelity 3D maps from sensor data. However, as the scale and complexity of the environment increase, neural SLAM approaches face renewed challenges in the back-end optimization process to keep up with runtime requirements and maintain global consistency. We introduce MISO, a hierarchical optimization approach that leverages multiresolution submaps to achieve efficient and scalable neural implicit reconstruction. For local SLAM within each submap, we develop a hierarchical optimization scheme with learned initialization that substantially reduces the time needed to optimize the implicit submap features. To correct estimation drift globally, we develop a hierarchical method to align and fuse the multiresolution submaps, leading to substantial acceleration by avoiding the need to decode the full scene geometry. MISO significantly improves computational efficiency and estimation accuracy of neural signed distance function (SDF) SLAM on large-scale real-world benchmarks.