Suppose the knight's permitted moves are $u$ and $v$. (These are two-dimensional "vectors" on the torus.) Then
after $N$ moves he is at $nu+(N-n)v$ for some $n$. We can write this as $Nv+n(u-v)$. Note that the first term is the same whatever $n$ may be; and note that choosing $n$ is all we get to do. So the knight's repertoire of available squares is, up to translation, just all the multiples of $u-v$. This will form a single straight line, possibly "dotted", and possibly wrapping around as it reaches the edges of the 100x100 square.
Without loss of generality, suppose one of his available moves is (2,1). Then his other might be:
(1,2), so that $u-v$ = (1,-1) and he can reach a diagonal line of 100 squares;
(1,-2), so that $u-v$ = (1,-3) and he can reach a more-slanted "dotted" line of 100 squares, wrapping around twice or three times depending on how you count;
(2,-1), so that $u-v$ = (0,2) and he can reach an orthogonal dotted line of 50 squares;
(-2,1), so that $u-v$ = (4,0) and he can reach an orthogonal more-dotted line of 25 squares;
(-2,-1), so that $u-v$ = (4,2), dotted, slanted, wrapping around once or twice depending on how you count, 50 squares;
(-1,2), so that $u-v$ = (3,1), dotted, slanted, wrapping 2/3 times, 100 squares;
(-1,-2), so that $u-v$ = (3,3), wrapping around on a single 45-degree diagonal, covering all 100 squares.