Quasi-two-dimensional (quasi-2D) materials hold promise for future electronics because of their unique band structures that result in electronic and mechanical properties sensitive to crystal strains in all three dimensions. Quantifying crystal strain is a prerequisite to correlating it with the performance of the device, and calls for high resolution but spatially resolved rapid characterization methods. Here we show that using fly-scan nano X-ray diffraction we can accomplish a tensile strain sensitivity below 0.001% with a spatial resolution of better than 80 nm over a spatial extent of 100 $mu$m on quasi 2D flakes of 1T-TaS2. Coherent diffraction patterns were collected from a $sim$ 100 nm thick sheet of 1T-TaS2 by scanning 12keV focused X-ray beam across and rotating the sample. We demonstrate that the strain distribution around micron and sub-micron sized bubbles that are present in the sample may be reconstructed from these images. The experiments use state of the art synchrotron instrumentation, and will allow rapid and non-intrusive strain mapping of thin film samples and electronic devices based on quasi 2D materials.