Polycrystalline samples of hcp He-4 of molar volume V-m = 19.5 cm(3) with small amount of He-3 impurities were grown in an annular container by the blocked-capillary method. Three concentrations of He-3, x(3), were studied: isotopically purified He-4 with the estimated x(3) <10(-10), commercial 'well-grade' helium with x(3) similar to 3.10(-7) and a mixture with x(3) = 2.5.10(-6). Torsional oscillations at two frequencies, 132.5 and 853.6 Hz, and thermal conductivity were investigated before and after annealing. The solid helium under investigation was located not only in the annular container but also in the axial fill line inside two torsion rods and dummy bob of the double-frequency torsional oscillator. The analysis of the frequency shifts upon loading with helium and changing temperatures of different parts of the oscillator suggests that the three techniques probe the properties of solid helium in three different locations: the two different torsion modes respond to the changes of the shear modulus of solid helium in either of the two torsion rods while the thermal conductivity probes the phonon mean free path in solid helium inside the annular container. The temperature and width of the torsional anomaly increase with increasing frequency and x(3). The phonon mean free path increases with increasing x(3). Annealing typically resulted in an increased phonon mean free path but often in little change in the torsional oscillator response. While the magnitude of the torsional anomaly and phonon mean free path can be very different in different samples, no correlation was found between them. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4765093]