Their cards say the can not use weapons and/or armour in battle.

But later expansions provide such items for use in psychic combat.

Would the Priest and Monk be able to use such items?

On a side note, the Minotaur card says he can not use armour suggesting he can not use armour in both battle and psychic combat.

Yes, they are just precluded from using such things in Battle, so they may use any that are for use in Psychic Combat.