We compute all the Chern, Milnor and Pontryagin numbers for canonical toric manifolds associated with abstract simplicial complexes and the Stiefel-Whitney numbers for their real counterparts. Applications include combinatorial characterizations of the unitary, oriented and unoriented bordism classes, new geometrical representatives of the unitary bordism ring generators, a combinatorial criterion for a canonical toric manifold to bound, as well as the dimension estimates for their immersions into euclidean spaces.