The practical utilization of soft nanocomposites as a strain mapping sensor in tactile sensors and artificial skins requires robustness for various contact conditions as well as low-cost fabrication process for large three dimensional surfaces. In this work, we propose a multi-point and multi-directional strain mapping sensor based on multiwall carbon nanotube (MWCNT)-silicone elastomer nanocomposites and anisotropic electrical impedance tomography (aEIT). Based on the anisotropic resistivity of the sensor, aEIT technique can reconstruct anisotropic resistivity distributions using electrodes around the sensor boundary. This strain mapping sensor successfully estimated stretch displacements (error of 0.54 +/- 0.53 mm), surface normal forces (error of 0.61 +/- 0.62 N), and multi-point contact locations (error of 1.88 +/- 0.95 mm in 30 mm x 30 mm area for a planar shaped sensor and error of 4.80 +/- 3.05 mm in 40 mm x 110 mm area for a three dimensional contoured sensor). In addition, the direction of lateral stretch was also identified by reconstructing anisotropic distributions of electrical resistivity. Finally, a soft human-machine interface device was demonstrated as a practical application of the developed sensor.