Up to now, the highest current densities of MgB2 superconducting wires have been obtained by the internal magnesium diffusion (IMD) method. MgB2 superconductors are especially suitable for DC or AC windings generating low or medium magnetic fields, where thermal stability and low AC losses are important issues. Mechanical, thermal and electrical parameters of the wires are strongly influenced by metallic materials used for the outer sheath. While highly electrical conductive sheath material is beneficial for thermally stable behaviour, it has a great effect on the generation of high eddy current losses. To minimize the contribution of eddy current losses, multi-core MgB2 wires with low purity Cu and Al sheaths were prepared by the IMD process and characterized in detail. Results of low temperature measurements are analysed and discussed in the present work.