The general term for any diagonal going top-left to bottom-right direction is $k$-diagonal where $k$ is an offset form the main diagonal.

$k=1$ is the superdiagonal, $k=0$ is the main diagonal, and $k=-1$ is the subdiagonal.

The general term for any diagonal going top-left to bottom-right direction is $k$-diagonal where $k$ is an offset form the main diagonal.

$k=1$ is the superdiagonal, $k=0$ is the main diagonal, and $k=-1$ is the subdiagonal.

According to Mathworld, the general term for the antidiagonals seems to be skew-diagonals.