This might be obvious but I think it might be better clarify it, if you slash at any with you sword (who has weakness due to antithesis) but the creature is an ooze who is immune to slashing I assume you would still no damage.
I assume a creature who is resistant to your attack but also vulnerable you would just apply both ?
Would anthesis make your weapon count as a crit (for vulnerability purposes) for a creature with vulnerability to critical hits (the un-killable zombie) ?