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.
Thus:
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.