The crystallographic and magnetic phase diagram of the n = 2 layered manganite La_2-2xSr_1+2xMn₂O₇ in the region x≥0.5 has been studied using temperature-dependent neutron powder diffraction. The magnetic phase diagram reveals a progression of ordered magnetic structures generally paralleling that of three-dimensional (3D) perovskites with similar electronic doping: A (0.5≤x≤0.66)→C (0.75≤x≤0.90)→G (0.90≤x≤1.0). However, the quasi-2D structure amplifies this progression to expose features of manganite physics uniquely accessible in the layered systems: (i) a "frustrated" region between the A and C regimes where no long-range magnetic order is observed; (ii) magnetic polytypism arising from weak interbilayer magnetic exchange in the type-C regime; and (iii) a tetragonal-to-orthorhombic phase transition whose temperature evolution directly measures ordering of d_3y2-r2 orbitals in the a-b plane. This orbital-ordering transition is precursory to type-C magnetic ordering, where ferromagnetic rods lie parallel to the b axis. These observations support the notion that e_g orbital polarization is the driving force behind magnetic spin ordering. Finally, in the crossover region between type-C and type-G states, we see some evidence for the development of local type-C clusters embedded in a type-G framework, directly addressing proposals of similar short-range magnetic ordering in highly doped La_1-xCa_xMnO₃ perovskites.