The Item Compendium says:
They [items] modify the the existing powers or abilities of the creature they are assigned to, and therefore also alter the cost of the creature.
Worded like this, it appears that certain prequisites for a number of powers might be relaxed or tightened depending on what items a creature may be carrying.
1) Cohort cost limit (16)
2) Intellect Devourer's Body Thief victim cost limit (50)
3) Summoned Reserve creature cost limits (various)
4) Tome of Vecna sacrifice cost (10)
1) Warband (including cohort choice) being legal before assigning any items should be both necessary and sufficient. So no help, no hindrance from items, right?
2) A lot more arbitrary case... I would go with the total cost (creature & item(s )). Suggestion: one (2 if victim is Unique) item of I-Devourer's choice (from either I-Devourer or victim) is retained by the stolen body (but cursed item(s ) first). If/When stolen body is destroyed enemy scores for I-Devourer & item it originally had (if any).
3) Quite arbitrary also... Based on the Item Compendium quote above I would say total cost determines whether a creature + item can stay in reserve and be summoned
4) Worth 10 points or more ... I think that wording can include item cost (after all, the sacrifice is worth those VPs to the opponent). So Elf Archer + Healing Potion is ok sacrifice, but Goblin Adept + Cursed Rot Scarab is not...
Somewhat related: I think "new creatures" (E g Thundertusk Cavalry: Persintent rider) can only be assigned items "on board" ( e g by Eternal Blade). Since "new creatures" are not in attendance at set-up no items can assigned to then nor be left "waiting" for them...