  With the $\Omega$-operators for the Virasoro algebra \cite{BF} and the super
Virasoro algebra in \cite{CL, CLL}, we get the $\Omega$-operators for the
Ovsienko-Roger superalgebras in this paper and then use it to classify all
simple cuspidal modules for the $\bZ$-graded and $\frac12\bZ$-graded
Ovsienko-Roger superalgebras. By this result, we can easily classify all simple
Harish-Chandra modules over some related Lie superalgebras, including the $N=1$
BMS$_3$ algebra, the super $W(2,2)$, etc.
