In this paper, we present four constructions of {general} self-orthogonal matrix-product codes associated with Toeplitz matrices. The first one relies on the {dual} of a known {general} dual-containing matrix-product code; the second one is founded on {a specific family of} matrices, where we provide an efficient algorithm for generating them {on the basis of Toeplitz matrices} and {it has an interesting application in producing new non-singular by columns quasi-unitary matrices}; and the last two ones are based on the utilization of certain special Toeplitz matrices. Concrete examples and detailed comparisons are provided. As a byproduct, we also find an application of Toeplitz matrices, which is closely related to the constructions of quantum codes.