Combined compression-tension strain sensors with a range of 1 micro to a maximum of 20 milli-strain based on non-uniform multiple-core-offset fibers have been realized. A large strain range with high resolution is ideal for monitoring deformation of steel structures where a large compressive and tensile strain co-exists. Thanks to core-offset splicing of non-uniform fiber segments, unique asymmetric waveguides reduce the degeneracy of each section, realizing a reflection spectrum with a large range and irregular shape. Furthermore, enhanced multi-mode interference induced from high-order modes in silica cladding and air results in the large strain range with high resolution in both compression and tension regions. The sensitivity of 7.93 pm/µe with a strain step of 1.7 µe is achieved for micro-strain measurement. For milli-strain measurement, a strain coefficient of 1.298 nm/me over a tensile strain of 13.2 me is realized; in the compressive strain case, a coefficient of -1.251nm/me over compression of 20.1 me is observed.