Let (V = {mathbb R}^{p,q}) be the pseudo-Euclidean vector space of signature ((p,q)), (pge 3) and (W) a module over the even Clifford algebra (C! ell^0 (V)). A homogeneous quaternionic manifold ((M,Q)) is constructed for any (mathfrak{spin}(V))-equivariant linear map (Pi : wedge^2 W rightarrow V). If the skew symmetric vector valued bilinear form (Pi) is nondegenerate then ((M,Q)) is endowed with a canonical pseudo-Riemannian metric (g) such that ((M,Q,g)) is a homogeneous quaternionic pseudo-Kähler manifold. If the metric (g) is positive definite, i.e. a Riemannian metric, then the quaternionic Kähler manifold ((M,Q,g)) is shown to admit a simply transitive solvable group of automorphisms. In this special case ((p=3)) we recover all the known homogeneous quaternionic Kähler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If (p>3) then (M) does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kähler manifolds. Then it is shown that for (q = 0) the noncompact quaternionic manifold ((M,Q)) can be endowed with a Riemannian metric (h) such that ((M,Q,h)) is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if (p>3). The twistor bundle (Z rightarrow M) and the canonical ({mathrm SO}(3))-principal bundle (S rightarrow M) associated to the quaternionic manifold ((M,Q)) are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution (mathcal D) of complex codimension one, which is a complex contact structure if and only if (Pi) is nondegenerate. Moreover, an equivariant open holomorphic immersion (Z rightarrow bar{Z}) into a homogeneous complex manifold (bar{Z}) of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any (mathfrak{spin}(V))-equivariant linear map (Pi : vee^2 W rightarrow V) a homogeneous quaternionic supermanifold ((M,Q)) is constructed and, moreover, a homogeneous quaternionic pseudo-Kähler supermanifold ((M,Q,g)) if the symmetric vector valued bilinear form (Pi) is nondegenerate.

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