The out-of-normal emission in cholesteric liquid-crystal lasers is studied experimental and theoretically. Apart from the well-known dominant laser in the direction of the helix axis, three other types of radiation, with cone-shaped spatial patterns, are identified and characterized. The physical mechanisms responsible for the different emissions are clarified. One of the radiations is a weak colorful lasing emission whose wavelength changes continuously depending on the propagation direction. The wavelengths of the other two radiations take place at the longwavelength and short-wavelength edges of the photonic bandgap. These emissions are attributed to an anomalous scattering phenomenon that gives rise to energy transfer from the main laser beam to some specific directions where the amount of final photonic states is high. An expression for the scattering cross section, reminiscent of Fermi's golden rule for spontaneous emission in photonic structures, is proposed. Some other phenomena independent of the lasing occurrence but driven by the anomalous scattering are briefly presented.