A particle's strangeness is the negative of the number of strange quarks minus the number of strange antiquarks, or -(n(strange) - n(antistrange)). Since a strange quark (which is what I assume you're talking about) has one strange quark and no strange antiquarks,
strangeness = -(1 - 0) = -1
Antimatter doesn't have negative mass, due to the fact that mass is a scalar quantity and is thus neither positive nor negative. However, properties that do have sign (e.g. spin and charge) are reversed in sign between a particle and its antiparticle.