The general term  for _any_ diagonal going top-left to bottom-right direction is [$k$-diagonal](https://en.wikipedia.org/wiki/Diagonal#Matrices) where $k$ is an offset form the main diagonal.

$k=1$ is the [superdiagonal](http://mathworld.wolfram.com/Superdiagonal.html),
$k=0$ is the main diagonal, and $k=-1$ is the [subdiagonal](http://mathworld.wolfram.com/Subdiagonal.html).

According to Mathworld, the general term for the antidiagonals seems to be [skew-diagonals](http://mathworld.wolfram.com/SkewDiagonal.html).