  Ground-state properties of layered nickelates are investigated based on the
orbital-degenerate Hubbard model coupled with lattice distortions, by using
umerical techniques. The N\'eel state composed of spin S=1 ions is confirmed in
the undoped limit x=0. At x=1/2, novel antiferromagnetic states, called CE- and
E-type phases, are found by increasing the Hund's coupling. (3 x^2 - r^2 / 3
y^2 - r^2)-type orbital ordering is predicted to occur in a checkerboard-type
charge-ordered state. At x=1/3, both Coulombic and phononic interactions are
found to be important, since the former stabilizes the spin stripe, while the
latter leads to the striped charge-order.
