The quantum Hall effects in sliding bilayer graphene and a AAB-stacked trilayer system are investigated using the Kubo formula and a generalized tight-binding model. The various stacking configurations can greatly diversify the magnetic quantization and thus create rich and unique transport properties. The quantum conductivities are very sensitive to the Fermi energy and magnetic-field strength. The diverse features cover the specific non-integer conductivities, the integer conductivities with distinct steps, the splitting-created reduction and complexity of quantum conductivity, a vanishing or non-zero conductivity at the neutral point, and the well-like, staircase, composite, and abnormal plateau structures in the field dependencies. Such stacking-dependent characteristics mainly originate from the crossing, anticrossing and splitting Landau-level energy spectra and three kinds of quantized modes.