To understand a terahertz (THz) response of a point contact device, a number of samples based on CdTe/CdMgTe quantum wells grown by a molecular beam epitaxy were investigated at low temperatures and high magnetic fields. The experiments involved magneto-transport, photocurrent, and transmission measurements carried out with monochromatic THz sources or a Fourier spectrometer. Samples of different geometry with and without gate metallization were used. We observed excitations of a two-dimensional electron plasma in the form of optically induced Shubnikov-de Haas oscillations, cyclotron resonance transitions, and magneto-plasmon resonances. A polaron effect was observed at magnetic fields higher than 10 T. A point contact device processed with an electron beam lithography was investigated as a detector of THz radiation. It was shown that the main mechanism responsible for a THz performance of the point contact was excitation of magneto-plasmons with a wavevector defined by geometrical constrictions of the device mesa.