WordNet sense 1 (enter a group or organization in order to spy on the members):

infiltrate

WordNet sense 2 (spread or diffuse through):

diffuse, imbue, permeate, pervade, riddle, interpenetrate, diffuse

WordNet sense 3 (pass into or through, often by overcoming resistance):

perforate

WordNet sense 4 (come to understand):

bottom, fathom

WordNet sense 5 (become clear or enter one's consciousness or emotions):

click, dawn, get through, get across, come home, fall into place, sink in