I think the first question that should have been asked is: If a wizard has an item that allows him to cast magic missle, can he use a different item as the implement to channel it?
Yes, he can, from what I understand, because Magic Missile is a Wizard power, irregardless of the Implement you use to enhance it.
So, for example, a Wizard could wield a +1 Wand of Magic Missile in one hand, and a +3 Orb in the other hand. he could activate the Wand's power to cast a Magic Missile, but use the Orb's bonus to hit and damage.
Thus far, I've found nothing that specifically says you can't do it, but also nothing that specifically says you can. I'll take another closer look, just in case.
If the answer is yes, then perhaps, through some combination of multiclassing and specific items that let priest use implements for arcane spells our cleric might have a chance,
That's true, but it really has nothing to do with example you present above.
To use Wizards as an example:
Implements
Wizards make use of orbs, staffs, and wands to help channel and direct their arcane powers. Every wizard has mastery of one type of implement (see “Class Features”). Without an implement, a wizard can still use his or her powers. A wizard wielding a magic orb, staff, or wand can add its enhancement bonus to the attack rolls and the damage rolls of wizard powers, as well as wizard paragon path powers, that have the implement keyword.
It doesn't specify where the wizard powers must come from... only that they must be wizard powers, and not powers from another class.
What's more the magic item section states:
In general, magic item powers follow the same rules as other powers (in that they have ranges, shapes, and so forth).
In the absence of any other evidence, it would lead me to believe you can "dual wield" two different implements at the same time -- one to activate a power or property and another to use its attack and damage enhancement on the activated power.
Likewise, a (Paragon-level) Wizard with a Staff of Fiery Might and a Wand of Fiery Bolt could activate the Wand to shoot a Fiery Bolt and then activate the Staff to reroll some of the Fiery Bolt's damage... All the while using the better enhancement bonus of the two.