Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of two-dimensional Dirac material, protected by nonsymmorphic symmetries, was recently proposed by S. M. Young and C. L. Kane [Phys. Rev. Lett. 115, 126803 (2015)10.1103/PhysRevLett.115.126803]. By breaking of time-reversal or inversion symmetry one can split the Dirac cones into Weyl nodes. The latter are characterized by local Chern numbers, which makes them two-dimensional analogs of Weyl semimetals. We find that the formation of the Weyl nodes is accompanied by an emergence of one-dimensional surface states, similar to Fermi arcs in Weyl semimetals and edge states in two-dimensional graphene. We explore these states for a quasi-one-dimensional nonsymmorphic ribbon. The type and strength of applied deformation control the location and Weyl nodes and their composition. This determines the properties of emerging edge states. The sensitivity of these edge states to the external deformations makes nonsymmorphic materials potentially useful as a new type of electromechanical sensor.