Comprehensive study of magnetic properties of the layer-ordered perovskites $\mathrm{N}{\mathrm{d}}_{1--x}\mathrm{C}{\mathrm{a}}_{x}\mathrm{B}{\mathrm{a}}_{1--y}\mathrm{L}{\mathrm{a}}_{y}\mathrm{C}{\mathrm{o}}_{2}{\mathrm{O}}_{5+\ensuremath{\delta}}$ is presented as a function of the site-selected charge doping $\mathrm{[}c=(x--y)/2+\ensuremath{\delta}\ensuremath{-}0.5,x\ensuremath{\le}0.2$ and $y\ensuremath{\le}0.1,0.07l\ensuremath{\delta}l0.84]$, oxygen disorder, and hydrostatic pressure $Pl10\phantom{\rule{0.16em}{0ex}}\mathrm{kbar}$. The single-phase oxygen-ordered orthorhombic phase exhibiting complex ferrimagnetic, antiferromagnetic, and metal-insulator phase transitions was found for a narrow oxygen range around $\ensuremath{\delta}\ensuremath{\sim}0.5\ifmmode\pm\else\textpm\fi{}0.1$. Significant difference between impact of hole $(cg0)$ and electron $(cl0)$ doping was observed depending on the site of cation substitution. Gradual enhancement of the Curie temperature ${T}_{\mathrm{C}}$ was observed over the whole range of $c$ to be unaffected by the local oxygen vacancy disorder. Maximum of the N\'eel temperature ${T}_{\mathrm{N}}$ at $c=0$ was found rapidly disappearing at $c=0.05$ for Ca/Nd substitution while it was maintained for La/Ba substitution, indicating that the oxygen vacancy disorder, especially for $\ensuremath{\delta}g0.5$, has a larger effect on antiferromagnetic phase than the charge doping. The temperature of metal-insulator transition ${T}_{\mathrm{MIT}}$ was found practically unchanged by either charge doping or disorder. The application of hydrostatic pressure slightly suppressed ${T}_{\mathrm{C}}$ and increased ${T}_{\mathrm{N}}$ by stabilization of the antiferromagnetic phase with the largest observed value of $\mathrm{d}{T}_{\mathrm{N}}/\mathrm{d}P=5.75\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{kbar}$. Complex magnetic behavior affected by hydrostatic pressure was accounted for by ferro- and antiferromagnetic interactions resulting from the charge separation and spin transitions.