We develop multi-band echo-volumar-imaging (MB-EVI) by combining multi-slab encoding with EVI to investigate BOLD sensitivity, resting-state connectivity in different frequency bands, and spatial-temporal resolution limits. We also study the effect of compressed sensing (CS) reconstruction on fMRI sensitivity. Mapping of major resting-state networks with 3mm3 voxel size was feasible in multiple frequency bands. High spatial resolution (2mm3) improved delineation of neuroanatomy and enabled sensitive mapping task-based activation. CS with 2.4-fold undersampling showed negligible loss in image quality and moderate region-specific losses in BOLD sensitivity. MB-EVI provides flexibility for maximizing spatial-temporal resolution, volume-coverage and BOLD-sensitivity for mapping task-activation and functional connectivity.