The effects of axial tensile and bending strains on the critical current densities of Ag and AgNiMg/Bi-2212 wires produced by the powder-in-tube method have been studied. At T=4.2 K and B=12 T the critical current densities of the investigated single and multicore wires exceeded 150 and 80 A mm(-2) (2 mu V cm(-1) offset criterion), respectively. The observed degradation of the critical current density due to strain effects is irreversible and can be attributed to the formation of microcracks within the superconducting core. In the case of Ag/Bi-2212 wires the axial tensile strain values epsilon(0.8) leading to a 20% reduction of the critical current density at 4.2 K and 12 T are around 0.2% for both single and multicore wires with seven filaments, whereas the epsilon(0.8) values for AgNiMg/Bi-2212 single and multicore wires exceed 0.5 and 0.8%, respectively. The bending strain experiments reveal a reduced sensitivity to strain effects for Ag/Bi-2212 wires with a larger fraction of Ag in the conductor cross-section. Bending at elevated temperatures has been found to affect the critical current density of Ag/Bi-2212 mono-core wires at lower strain levels than axial tensile strains applied at 4.2 K. The strain leading to an irreversible reduction of the critical current density seems to be determined mainly by the residual thermal strains. Finally, results of mechanical properties of the composite wires at 4.2 K are presented. The Young's modulus of the composite wires is nearly the same for the two sheath materials, whereas the yield strengths sigma(0.2), are very different. For Ag and AgNiMg/Bi-2212 single core wires, the average sigma(0.2) values at 4.2 K are 46 and 89 MPa, respectively.