Self-orthogonal codes are a significant class of linear codes in coding theory and have attracted a lot of attention. In [20], [26],p-ary self-orthogonal codes were constructed by usingp-ary weakly regular bent functions, wherepis an odd prime. In [42], two classes of non-degenerate quadratic forms were used to construct q-ary self-orthogonal codes, whereqis a power of a prime. In this paper, we construct new families ofq-ary self-orthogonal codes using vectorial dual-bent functions. Some classes of at least almost optimal linear codes are obtained from the dual codes of the constructed self-orthogonal codes. In some cases, we completely determine the weight distributions of the constructed self-orthogonal codes. From the view of vectorial dual-bent functions, we illustrate that the works on constructing self-orthogonal codes fromp-ary weakly regular bent functions [20], [26] and non-degenerate quadratic forms withqbeing odd [42] can be obtained by our results. We partially answer an open problem on determining the weight distribution of a class of self-orthogonal codes given in [42]. As applications, we construct new infinite families of at least almost optimalq-ary linear complementary dual codes (for short, LCD codes) and quantum codes.