Most of the Named Unique Passives have the same value on different items, so it doesn't matter which one is used.
Spellblade is an exception. Basically, the damage to a single target goes in the priority Lichbane > Trinity Force > Iceborn Gauntlet. However, if you have Iceborn Gauntlet and either Lichbane or Trinity Force, you still get the AoE slow and damage from Iceborn Gauntlet, with only the damage to the target of the autoattack overridden.
For Mana Charge, only a single Tear of the Goddess item will charge at a time. When one reaches maximum charge, it has to be upgraded before others will stack. (IIRC, anyways)
Named Unique Actives share a cooldown. For example, if you have both Mercurial Scimitar and Quicksilver Sash, using either will put both on cooldown.
If the unique passive has different values (for example, Machete and Skirmisher's Sabre "Jungler" passive), then it should take the highest value.