Features of the radiation spectra are investigated with the quantum electrodynamic theory for the nonlinear scattering interaction between relativistic electron and few-cycle linearly polarized laser pulse. The angle between the moving direction of the electron and that of the laser pulse affects the scattered radiation characteristics. When the electron has a head-on collision with the laser pulse having a carrier envelope phase as zero, the angular distribution of the scattered radiation spectrum is symmetrical with respect to the laser pulse propagation direction. Such a symmetry disappears when the electron collides with the laser obliquely and the direction of most of the radiation energy shifts at an acute angle towards the electron direction. The CEP has significant effects on the spectral angular distribution. The CEP influence is determined by the exertion of the electromagnetic field on the motion of the electron, whose trajectory overlap in phase space leads to the interference between scattered radiation in different intervals of the interaction process. The supercontinuum radiation could be produced under certain CEPs. An external electrostatic field applied as the environment for the laser-electron interaction is another important factor affecting the scattered radiation features by modulating the harmonic components and their angular distribution. This study may help the analysis of the spectral data from relativistic laser-solid target experiments.