  The recombination model is applied to the production of $K, \phi, \Lambda$
and $\Omega$ at all $p_T$ in central Au+Au collisions. The thermal-shower
component of the recombination is found to be important for $K$ and $\Lambda$,
but only in a minor way for $\phi$ and $\Omega$ in the intermediate to high
$p_T$ region. The normalization and inverse slope of the thermal partons in the
strange sector are determined by fitting the low-$p_T$ data. At higher $p_T$
the data of $K, \phi, \Lambda$ and $\Omega$ in the log scale are all well
reproduced in our study that extends the thermal contribution and includes the
shower contribution. The calculated result on the $\Lambda/K$ ratio rises to a
maximum of around 2 at $p_T\approx 4$ GeV/c, arching over the data in linear
scale. The production of $\phi$ and $\Omega$ are shown to arise mainly from the
recombination of thermal partons, thus exhibiting exponential $p_T$ dependences
in agreement with the data. Their ratio, $R_{\Omega/\phi}$, rises linearly to
$p_T\approx 4$ GeV/c and develops a maximum at $p_T\approx 5.5$ GeV/c. It is
argued that the $p_T$ spectra of $\phi$ and $\Omega$ reveal directly the
partonic nature of the thermal source that characterizes quark-gluon plasma.
Comments are made on the $\Omega$ puzzle due to the simultaneous observation of
both the exponential behavior of the $\Omega$ spectrum in $p_T$ and the
existence of low-$p_T$ particles associated with $\Omega$ as trigger.
