A first principles study of La2-2xSr1+2xMn2O7 compounds for doping levels 0.3 < or = x < or = 0.5 shows that the low energy electronic structure of the majority spin carriers is determined by strong momentum-dependent interactions between the Mn eg dx2-y2 and d3z2-r2 orbitals, which, in addition to an x-dependent Jahn-Teller distortion, differ in the ferromagnetic and antiferromagnetic phases. The Fermi surface exhibits nesting behavior that is reflected by peaks in the static susceptibility, whose positions as a function of momentum have a nontrivial dependence on x.