The climbing microrobots have attracted growing attention due to their promising applications in exploration and monitoring of complex, unstructured environments. Soft climbing microrobots based on muscle-like actuators could offer excellent flexibility, adaptability, and mechanical robustness. Despite the remarkable progress in this area, the development of soft microrobots capable of climbing on flat/curved surfaces and transitioning between two different surfaces remains elusive, especially in open spaces. In this study, we address these challenges by developing voltage-driven soft small-scale actuators with customized 3D configurations and active stiffness adjusting. Combination of programmed strain distributions in liquid crystal elastomers (LCEs) and buckling-driven 3D assembly, guided by mechanics modeling, allows for voltage-driven, complex 3D-to-3D shape morphing (bending angle > 200°) at millimeter scales (from 1 to 10 mm), which is unachievable previously. These soft actuators enable development of morphable electroadhesive footpads that can conform to different curved surfaces and stiffness-variable smart joints that allow different locomotion gaits in a single microrobot. By integrating such morphable footpads and smart joints with a deformable body, we report a multigait, soft microrobot (length from 6 to 90 mm, and mass from 0.2 to 3 g) capable of climbing on surfaces with diverse shapes (e.g., flat plane, cylinder, wavy surface, wedge-shaped groove, and sphere) and transitioning between two distinct surfaces. We demonstrate that the microrobot could navigate from one surface to another, recording two corresponding ceilings when carrying an integrated microcamera. The developed soft microrobot can also flip over a barrier, survive extreme compression, and climb bamboo and leaf.