  This paper considers a family of finite dimensional simple Lie superalgebras
of Cartan type over a field of characteristic $p>3$, the so-called special odd
contact superalgebras. First, the spanning sets are determined for the Lie
superalgebras and their relatives. Second, the spanning sets are used to
characterize the simplicity and to compute the dimension formulas. Third, we
determine the superderivation algebras and the first cohomology groups.
Finally, the dimension formulas and the first cohomology groups are used to
make a comparison between the special odd contact superalgebras and the other
simple Lie superalgebras of Cartan type.
