We analyze the results of numerically exact modeling of scattering and absorption characteristics of randomly oriented polydisperse spheroidal soot particles covered by spheroidal nonabsorbing sulfate shell. Using numerically exact T-matrix method, at wavelengths 0.355 mu m, 0.532 mu m and 1.064 mu m, we perform computations of the absorption cross section (Cabs), absorption angstrom ngstrom exponent (AAE), backscattering linear depolarization ratio (LDR) and scattering matrix elements for spheroids with core volume-equal-sphere effective radius (further in the text, the term "effective radius" is used) Rc,eff = 0.1, 0.15 mu m, soot volume fraction .f = 7% and 15%. Mostly, we consider the case of oblate spheroids with the axis ratio epsilon ranging from 1.1 to 1.8. Our size-averaged results demonstrate, in particular, that: (i) the absorption cross section depends on the degree of nonsphericity very weakly, but substantially increases with increasing aerosol size and decreases with increasing wavelength; (ii) the absorption angstrom ngstro center dot m exponent also shows a weak dependence on the spheroid axis ratio, but it is quite sensitive to the choice of the wavelength pair, particle size and amount of soot/sulfate; (iii) the backscattering linear depolarization ratio is very sensitive to particle nonsphericity, size, amount of sulfate coating and wavelength, and concentric soot-sulfate spheroidal particles could cause a wide range of the LDR values that significantly decrease with increasing wavelength. We also conclude that at backscattering angles, the elements of the normalized scattering matrix exhibit specific changes which depend on particle shape, size, and amount of coating material.