Three-dimensional topological semimetals have emerged as strong candidates to probe new fundamental physical phenomena that could be exploited to develop next generation electronics. However, many aspects of their electronic properties remain unclear. This thesis addresses mainly two of them: (i) the interplay between their lattice deformations and charge carrier dynamics and (ii) the possible origin of their magnetoresistive behaviour. This is done by investigating the transport properties of microstructures fabricated with the focused ion beam. The results are presented in three main parts: In the first part, I describe the development of an apparatus for the controlled application of strain gradients at cryogenic temperatures. This is achieved by mechanically bending 3D crystalline cantilevers. A simple sample design aimed at transport characterization under strain is adopted. The bending apparatus is also fitted to a rotator probe for the simultaneous application of strain gradients and the rotation with respect to the applied magnetic field. Strain gradients exceeding 1.3 % um^-1 are achieved at a surface strain value of approx. 0.65 %. Moreover, the results establish that the quantum transport characteristics of the cantilevers are unaltered by the large strain gradients, demonstrating that no plastic deformation is induced. In the second part, I apply the newly developed technique to explore the effects of strain gradients on the Dirac semimetal Cd3As2. This material hosts novel electron orbits, called Weyl orbits, that combine bulk chiral states coming from Landau quantization with Fermi arc states that are located on the surface. Theoretical models that treat strain gradients in the framework of pseudo-electromagnetic fields predict that the periodicity of the Weyl orbits is sensitive to strain gradients. Despite features of the experimental data compatible with some of the expected effects of pseudo-fields, the results reveal a more complicated experimental scenario with important aspects that cannot be easily captured by the available simplified models. In the final part, I investigate the transport properties of the Dirac nodal arc semimetal PtSn4. This material is characterized by its extremely large magnetoresistance at low temperatures. There has been an intense debate on whether such behaviour is connected to its peculiar electronic structure that contains a short Dirac node line in momentum space associated to graphene-like surface states. By fabricating the first microstructures of this material, I study the transport behaviour for currents applied along all main crystallographic directions. While for some directions the usual extremely large magnetoresistance is observed, for one particular direction the magnetoresistance is suppressed. An inspection of the complex Fermi surface shows that this suppression is associated to the existence of open orbits in one of the branches. The presence of the open orbits is very sensitive to the magnetic field orientation. These results suggest a semi-classical origin for the characteristic large magnetoresistance observed in this material.