My initial selection for a set of people who would fit this criteria while providing interesting character conflict was to have Lelouch Lamperouge (from Code Geass) as the bow, Itachi Uchiha (from Naruto) as the sword, Taylor Hebert (from Worm) as the shield, and for the fun of having a foil who is an actual hero instead of an almost-villain, Aerith Gainsborough (from FFVII) as the spear.
The way the Cardinal Heroes world works would completely shut down Taylor's power. At best, she would get her powers back during the Waves. She'd have to hope her affinity is related to how her power works to get even a shadow of her previous ability, and it will be limited by her MP/SP or whatever else.
Internal powers will work. If the power is used to hurt others or do something like harden your skin, then the base stats and stat modifications from the Holy Weapons will negate, gimp or improve(HA, fat chance) the power.
Depending if the Geass is completely internal, rather than a connection to him from CC to where ever it originally originated from, his power should work as usual on the common masses, with certain people potentially being resistant to it. Just because the Geass basically has no counter in its own world doesn't mean the people of other worlds can't defend against it.
Itachi could probably just do everything he did before, depends if Chakra is similar to that energy Hengen Musou uses AKA Life Force, with external use of it potentially weakened and him not getting the benefits of the level system when using it.
For Aerith, materia usage would be cut off, magic Ancients use just won't work because the Planet is just plain different and doesn't operate the same way, and depending on how much support she'd need from her ancestors, she might be able to do something with Dragon Vein style casting.