The strangeness degrees of freedom in the parton structure of the nucleon are explored in the global analysis framework, using the new CTEQ6.5 implementation of the general mass perturbative QCD formalism of Collins. We systematically determine the constraining power of available hard scattering experimental data on the magnitude and shape of the strange quark and anti-quark parton distributions. We find that current data favor a distinct shape of the strange sea compared to the isoscalar non-strange sea. A new reference parton distribution set, CTEQ6.5S0, and representative sets spanning the allowed ranges of magnitude and shape of the strange distributions, are presented. Some applications to physical processes of current interest in hadron collider phenomenology are discussed.