We present our theoretical results on the ground states in layered triangular-lattice compounds ANiO2 (A=Na, Li, Ag). To describe the interplay between charge, spin, orbital, and lattice degrees of freedom in these materials, we study a doubly-degenerate Hubbard model with electron-phonon couplings by the Hartree-Fock approximation combined with the adiabatic approximation. In a weakly-correlated region, we find a metallic state accompanied by √ 3 × √ 3 charge ordering. On the other hand, we obtain an insulating phase with spin-ferro and orbital-ferro ordering in a wide range from intermediate to strong correlation. These phases share many characteristics with the low-temperature states of AgNiO2 and NaNiO2, respectively. The charge-ordered metallic phase is stabilized by a compromise between Coulomb repulsions and effective attractive interactions originating from the breathing-type electronphonon coupling as well as the Hund's-rule coupling. The spin-orbital-ordered insulating phase is stabilized by the cooperative effect of electron correlations and the Jahn-Teller coupling, while the Hund'-rule coupling also plays a role in the competition with other orbital-ordered phases. The results suggest a unified way of understanding a variety of low-temperature phases in ANiO2. We also discuss a keen competition among different spin-orbital-ordered phases in relation to a puzzling behavior observed in LiNiO2.