SUR and VAR are both estimators for simulatneous equation system. However, they are applied for different purposes. The main puspose to use SUR is to increase estimation efficiency by taking advantage of the variance-covariance structure of the error term. The use of VAR is mainly for the time series dependence of relationship between "endogenous" variables.
Impulse response is applied to VAR, which tracts how each explained "endogenous" variable (in a VAR system) respponds to shocks over time.