Well, in the aforementioned traditions, oil is/was typically used to reduce your opponent's ability to grasp and/or hold you so as to reduce the odds of being pinned, so this would be of mitigated use in a fight involving bladed weapons.

Loincloths are likely as much a way to prove you aren't wearing any armour as Blizzard's way of preserving the combatants' modesty at least somewhat, given that Greek wrestling, for example, had the combatants fight completely nude.