Answer
$m$ is not an odd integer and/or $n$ is not odd integer.
Work Step by Step
We set $A$ to refer to "$m$ is an odd integer" and $B$ to refer to "$n$ is an odd integer". Now, we have $A$ and $B$ as true. The negation of $A$ and $B$ will be false, that is, at least one of them is not odd. Thus, we can say:
$m$ is not an odd integer and/or $n$ is not an odd integer.