The SCUBA polarized 850um thermal emission data of the OMC-2 region in Orion A are added to and homogeneously reduced with data already available in the OMC-3 region. The data set shows that OMC-2 is a region generally less polarized than OMC-3. Where coincident, most of the 850um polarization pattern is similar to that measured in 350um polarization data. Only 850um polarimetry data have been obtained in and around MMS7, FIR1 and FIR2, and in the region south of FIR6. A realignment of the polarization vectors with the filament can be seen near FIR1 in the region south of OMC-3. An analysis shows that the energy injected by CO outflows and H2 jets associated with OMC-2 and OMC-3 does not appear to alter the polarization patterns at a scale of the 14" resolution beam. A second-order structure function analysis of the polarization position angles shows that OMC-2 is a more turbulent region than OMC-3. OMC-3 appears to be a clear case of a magnetically dominated region with respect to the turbulence. However, for OMC-2 it is not clear that this is the case. A more in-depth analysis of five regions displayed along OMC-2/3 indicates a decrease of the mean polarization degree and an increase of the turbulent angular dispersion from north to south. A statistical analysis suggests the presence of two depolarization regimes in our maps: one regime including the effects of the cores, the other one excluding it.