Very recently, the gravitational wave (GW) event GW170817 was discovered to be associated with the short gamma-ray burst (GRB) 170817A. Multi-wavelength follow-up observations were carried out, and X-ray, optical and radio counterparts to GW170817 were detected. The observations undoubtedly indicate that GRB170817A originates from a binary neutron star (BNS) merger. However, the GRB falls into the low-luminosity class which could have a higher statistical occurrence rate and detection probability than the normal (high-luminosity) class. This implies a possibility that GRB170817A is intrinsically powerful but we are off-axis and only observe its side emission. In this paper, we provide a timely modeling of the multi-wavelength afterglow emission from this GRB and the associated kilonova signal from the merger ejecta, under the assumption of a structured jet, a two-component jet, and an intrinsically less-energetic quasi-isotropic fireball respectively. Comparing the afterglow properties with the multi-wavelength follow-up observations, we can distinguish between these three models. Furthermore, a few model parameters (e.g., the ejecta mass and velocity) can be constrained.