We use world-line methods for pseudo-supersymmetry to construct sl(2|1)-invariant actions for the (2, 2, 0) chiral and (1, 2, 1) real supermultiplets of the twisted D-module representations of the sl(2|1) superalgebra. The derived one-dimensional topological conformal σ-models are invariant under nilpotent operators. The actions are constructed for both parabolic and hyperbolic/trigonometric realizations (with extra potential terms in the latter case). The scaling dimension λ of the supermultiplets defines a coupling constant, 2λ + 1, the free theories being recovered at λ = − 1 2 . We also present, generalizing previous works, the D-module representations of one-dimensional superconformal algebras induced by N = (p, q) pseudo-supersymmetry acting on (k, n, n − k) supermultiplets. Besides sl(2|1), we obtain the superalgebras