Elastoresistance describes the relative change of a material's resistance when strained. It has two major contributions: strain induced geometric and electronic changes. If the geometric factor dominates, like in ordinary metals such as copper, the elastoresistance is positive and rather small, i.e. typically of order 1. In a few materials, however, changes in electronic structure dominate, which gives rise to larger and even negative values, such as (-11) for Bi. Here, we report that the transition metal dichalcogenide (TMDC) WTe2 is a member of the second group, exhibiting a large and non-monotonic elastoresistance that is about (-20) near 100 K and changes sign at low temperatures. We discover that an applied magnetic field has a dramatic effect on the elastoresistance in WTe2: in the quantum regime at low temperatures, it leads to quantum oscillations of the elastoresistance, that ranges between (-80) to 120 within a field range of only half a Tesla. In the semiclassical regime at intermediate temperatures, we find that the elastoresistance rapidly increases and changes sign in a magnetic field. We provide a semi-quantitative understanding of our experimental results using a combination of first-principle and analytical low-energy model calculations. Understanding bulk properties of TMDCs under uniaxial strain is an important stepping stone toward strain engineering of 2D TMDCs.