Do all variables in a VAR/VEC need to be normally distributed, or only the target variable? It is very hard to get all of them to meet criteria of normality without deleting too many outliers.
Unless the assumptions of regression modeling have changed, there is no stipulation about the distributions of the variables in the model -- normal or otherwise. There are some technical assumptions about the behavior of the residuals from the model but even those are subject to interpretation in the "art and practice" of modeling.
This CV thread ( What is a complete list of the usual assumptions for linear regression? ) contains an excellent discussion of the various ins and outs of these assumptions. In particular, the comments between @AndyW and WHuber are illuminating. AndyW states, "There is no cook book, nor should there be given the potential variety of situations that linear regression could encompass." Which Whuber challenges, noting that he's extending the discussion into the "art and science" realm.