We report on tailoring magnetic properties and giant magneto-impedance GMI in glasscoated microwires fabricated by the Taylor-Ulitovsky method, by means of selection of their alloy composition and/or annealing conditions. Fe-rich microwires subjected to stress annealing show the hysteresis loops of inclined form due to induced transverse magnetic anisotropy, and hence become suitable for GMI. The transverse anisotropy depends on the annealing conditions: temperature, duration and stress. The application of external stress further drastically changes the shape of the hysteresis loops and the GMI spectra. The wires with compositions Co-Fe-Ni-Si-B and Co-Fe-Cr- Si-B are demonstrated to have a low Curie temperature (below 90oC) and pronounced temperaturedependent magnetic properties and GMI effect. Both families of developed microwires are foreseen for applications in high performance stress and temperature sensors as well as in tuneable sensory composite materials. Such composites contain short pieces of microwires embedded into a dielectric matrix and contribute to the effective ac permittivity. The latter depends on the wire magnetic properties through the GMI effect and can be tailored to produce a microwave response sensitive to environment: magnetic field, stress and temperature.