  We compute the rank of the group of central units in the integral group ring
$\Z G$ of a finite strongly monomial group $G$. The formula obtained is in
terms of the strong Shoda pairs of $G$. Next we construct a virtual basis of
the group of central units of $\Z G$ for a class of groups $G$ properly
contained in the finite strongly monomial groups. Furthermore, for another
class of groups $G$ inside the finite strongly monomial groups, we give an
explicit construction of a complete set of orthogonal primitive idempotents of
$\Q G$.
  Finally, we apply these results to describe finitely many generators of a
subgroup of finite index in the group of units of $\Z G$, this for metacyclic
groups $G$ of the form $G=C_{q^m}\rtimes C_{p^n}$ with $p$ and $q$ different
primes and the cyclic group $C_{p^n}$ of order $p^n$ acting faithfully on the
cyclic group $C_{q^m}$ of order $q^m$.
