We investigate effects of a non-magnetic impurity on zerogap state of molecular conductor α-(BEDT-TTF)2I3 and predict theoretically incommensurate oscillations of charge density. These oscillations reflect unique properties of the massless Dirac fermions, which are characterized by the incommensurate momenta ±κo of the contact points and the singular momentum distributions of the charge density. We examine an effective Hamiltonian in the presence of stripe charge ordering, neighboring the zerogap state. The energy bands are divided into two parts, having one-dimensional fermions and two-dimensional fermions. The one-dimensional-like bands exhibit a unique anisotropic dispersion which is linear along b-axis (parallel to the stripe) and parabolic along the a-axis (the stacking axis). Thus we expect anomalous magnetoresistance in stripe charge ordering state, since such a anisotropic dispersion indicates the unconventional Landau quantization.