We study the spin dynamics in a high-mobility two dimensional electron gas (2DEG) system with generic spin-orbit interactions (SOIs). We derive a set of spin dynamic equations which capture the purely exponential to the damped oscillatory spin evolution modes observed in different regimes of SOI strength. Hence we provide a full treatment of the D'yakonov-Perel's mechanism by using the microscopic linear response theory from the weak to the strong SOI limit. We show that the damped oscillatory modes appear when the electron scattering time is larger than half of the spin precession time due to the SOI, in agreement with recent observations. We propose a new way to measure the scattering time and the relative strength of Rashba and linear Dresselhaus SOIs based on these modes and optical grating experiments. We discuss the physical interpretation of each of these modes in the context of Rabi oscillation. In the finite temperature, We study the spin dynamics in the presence of impurity and electron-electron (e-e) scattering in a III-V semiconductor quantum well. Starting from the Keldysh formalism, we develop the spin-charge dynamic equation at finite temperature in the presence of inelastic scattering which provide a new approach to describe the spin relaxation from the weak to the strong spin-orbit coupling (SOC) regime. In the weak SOC regime, our theory shows that when the system is near the SU(2) symmetry point, because the spin relaxation due to DP mechanism is suppressed dramatically, the spin relaxation is dominated by the Elliott-Yafet (EY) mechanism in a wide temperature regime. The non-monotonic temperature dependence of enhanced-lifetime of spin helix mode is due to the competition between the DP and EY mechanisms. In the strong SOC regime, the our theory is consistent to the previous theoretical results at zero temperature.