The crystal structure, vibrational spectra and magnetic structure of quasi-two-dimensional layered van der Waals antiferromagnet CrSBr were studied by means of X-ray diffraction (XRD) and Raman spectroscopy at high pressures up to 33 GPa and ambient temperature, and neutron diffraction (ND) up to 5.7 GPa in the temperature range 10 – 300 K, respectively. The orthorhombic crystal structure of symmetry, observed at ambient pressure, remains stable at pressures up to 8 GPa, according to the XRD and Raman data. At ambient pressure, the A-type AFM order is formed in the initial orthorhombic phase below = 133 K. Application of high pressure leads to a suppression of the A-type AFM order. The Néel temperature decreases sharply to 93 K by 30 % and Cr ordered magnetic moment values are reduced from 3.1 to 2.0 in the pressure range 0 – 5.7 GPa, as found from the ND experiments. The effects of pressure-controlled compressive intralayer biaxial lattice strain and interlayer uniaxial lattice strain along the axis on the magnetic state of CrSBr are analyzed. The evaluated relationship between variation of the biaxial lattice strain and observed modification of the value via tuning of structural parameters point to its important role in tuning of magnetic properties. Upon further compression, a complex sequence of structural phase transitions at 8, 16, and 28 GPa was detected from XRDand Raman measurements. The first possible phase transition at 8 GPa is accompanied by anomalies in pressure behavior of lattice parameters and softening of the lowest frequency vibrational mode of A symmetry. The second phase transition at 16 GPa was associated with appearance of the (1/2 0 1) superstructure peak in the XRD spectra and extra modes in Raman spectra, pointing to a formation of the structural modification with the supercell doubled along the axis. The third phase transition at 28 GPa is accompanied by disappearance of the superstructure peak in the XRD spectra, implying breakdown of the supercell back to initial cell geometry. All the observed phases of CrSBr demonstrate pseudo-orthorhombic character and they are structurally similar, as found from the XRD data. A possible appearance of a subtle monoclinic distortion in the high pressure phases could not be excluded due to observation of extra Raman modes above and transition pressures. The present experimental information is important for further clarification of possible microscopic mechanisms for control of magnetic states of CrSBr and relevant vdW materials by application of high external pressures or strain engineering.