We have studied the step bunching properties of Si and SiGe layers on vicinal Si(113) substrates and the self-organized formation and spatial correlation of SiGe wire and island structures induced by such surface steps. The parameters for MBE growth have been varied systematically in order to investigate the self-assembling and self-ordering mechanisms appearing in growth of strained SiGe layers on vicinal surfaces. The nanostructures are analyzed by atomic force microscopy (AFM), transmission electron microscopy (TEM) and micro Raman spectroscopy. Si(113) substrates have a low surface energy which is comparable to Si(001) but show a much stronger tendency for bunching of steps on vicinal surfaces. The Si(113) surface reveals step bunches which are mainly multiples of a 4-atomic step unit. Periodic arrays of SiGe wires form by strain-mediated self-organization during deposition of a SiGe/Si multilayer. The correlation of wires in different layers is inclined with respect to the growth direction. This is well described by a model calculation assuming the Si surface steps to locate at the maxima of local strain. Ge islands nucleate preferentially at the step edges of vicinal Si(113) substrates and form ordered rows of islands. No Ge islands but wire-like Ge accumulations are observed at the step edges of the step bunched SiGe/Si multilayer buffers.