Precise manipulation of electronic band structures of two-dimensional (2D) transition metal dichalcogenides and oxides (TMD&Os) via localised strain engineering is an exciting avenue for exploiting their unique characteristics for electronics, optoelectronics, and nanoelectromechanical systems (NEMS) applications. This work experimentally demonstrates that mechanically-induced electrical transitions can be engineered in quasi-2D molybdenum disulphide (MoS2) and molybdenum trioxide (MoO3) using an in situ electrical nanoindentation technique. It is shown that localised strains on such quasi-2D layers can induce carrier transport alterations, thereby changing their electrical conduction behaviour. Such strain effects offer a potential tool for precisely manipulating the electronic transport properties of 2D TMD&Os, and understanding the interactions of the atomic electronic states in such layered materials.