Maximun distance that can be reached
Addition of vectors is commutative, so the order of moves is irrelevant. For example:

$(0,2) + (3,1) + (2,-2) = (0,2) + (2,-2) + (3,1) = (3,1) + (0,2) + (2,-2) = (5,1)$

So a simple brute force method is to calculate the distance traveled for all subsets of the set of $n$ possible moves. There are $2^n$ such subsets, but you don't need to consider the empty set. So the size of your search space is actually $2^n-1$.