  This paper is devoted to a study of the automorphism groups of three series
of finite dimensional special odd Hamiltonian superalgebras $\mathfrak{g}$ over
a field of prime characteristic. Our aim is to characterize the connections
between the automorphism groups of $\mathfrak{g}$ and the automorphism groups
of the corresponding underlying superalgebras. Precisely speaking, we embed the
former into the later. Moreover, we determine the images of the normal series
of the automorphism groups and homogeneous automorphism groups of
$\mathfrak{g.}$
