If the party isn't allowed weapons, then that should also affect IMPLEMENTS. Yes, wands, orbs, staves, rods - all checked at the door. Perhaps the cleric gets to keep his symbol, but that's not too bad. Now everyone is gimped a bit in combat - and you can lower difficulty across the board and 'ad hoc' xp to normal. You could allow players to improvise even implements with suitable penalties.
Implemens, outside of the Wizard class feature, are only useful if they have a magic bonus. Any implement power can be done unarmed.
Lacking weapons, on the other hand, causes players to lose out on the 2 or 3 point proficiency bonus, a lot of the damage, and in the case of the rogue, many of their powers and class features [which require light blade, crossbow or sling]
So, while the wizard loses his implement mastery feature, the other classes have their AC drop, their ability to hit with weapon attacks drop, their damage output drop, etc.
Everyone 'loses' their magic items in this scenario, but the wizard [and warlock] walks away with nearly everything intact, while the paladin and fighter are unable to do their 'jobs' as defenders, and the rogue better have stashed a dagger on his person to be able to do his.
One thing to point out ... with limited healing resources per combat, it is possible for the party to be weaker with a "nearly useless" paladin than with it. Unless they are willing to allow the paladin to die without healing him, the resources they need to spend on keeping him alive will not be "worth" the little damage he can dish out.
The monster stats assume certain ranges of AC, as well as certain ranges of "to hit" modifiers. A characters role is in part determined by their relative AC. Controllers and Strikers have around 14-16, the Leader likely has 16-17, while the shielded defender has 19-20. Marking allows a defender to "shield" his allies, giving them effectively the +2 bonus that the heavy sheild provides. When you remove the armor, many of the ones wearing heavy armor drop to having the lowest AC in the party, 10-12, making the wizard and anyone with comparable Dex [some of the strikers] or Int [a tactical warlord perhaps].
From a player perspective ... a weaponless/armorless party should avoid combat at all costs, unless they feel the wizard [maybe the rogue if he has found a dagger] can take out a small enounter easily and on their own. If they can find enough gear to at least have some passable [if sub optimal] weapons and armor, then at least they can fight as a group.
Chain, light shields, short swords ... the paladin/fighter won't have great AC [17], or greater damage output, but at least they can still do their job as defenders if it comes down to that. Even without armor check penalties, those trained in stealth wth a good dex will have a stealth that is 7 or more "better" than the paladin. It is probably not going to make the difference between success and failure. [There may be non skill check related reasons, such as disguises ... however there should be ways to have some sort of armor involved in a disguise ... unless they are invading a monastary and everyone needs to be in robes].
EDIT: Also, it is the scenario/DM that "intends" [as the original poster put it] for them to be out of armor. It's not a player choice at this point. It is one thing for the players to choose that he best course of action is to strip [say, for example, the paladin needs to do something underwater ... they don't want to risk drowning in their fullpate, a scenario common in 3.5 situations] than it being forced on the player. I'm sure the OP would have recieved slightly different feedback if he was asking how to address his players making the decision to go without armor, instead of how to address his decision to have them go without armor.