No, they are not protected
Diffusion Sliver's ability is only triggered when a Sliver becomes a 'target'. A creature is only targeted by spells or abilities that actually have the word 'target' on it. For instance, Giant Growth. From the Comprehensive rules:
114.1a An instant or sorcery spell is targeted if its spell ability identifies something it will affect by using the phrase “target [something],”
(Note that rule 114 in its entirety describes 'targeting', this is just a specific excerpt for instants and sorceries.)
The Sliver needs to be identified as that 'target [something]' in order for this specific ability to trigger. On instants and sorceries, this is spelled out; casting an Aura (ie Unholy Strength) on a Sliver also triggers the ability added to it by Diffusion Sliver, as they have an implicit target:
114.1b Aura spells are always targeted.
Casting an equipment would not trigger the ability, as they enter play unattached and not targeting anything. Their equip-ability however would count as becoming a target.
To look a little closer at what spells do and do not target the Slivers:
No, the key word here is "target". Your slivers get an ability that triggers whenevery a spell or ability gets cast/activated that contains the word "target", e.g. Doom Blade. Any spells/abilities which do not "target" your slivers are uneffected by diffusion sliver, as here in your example edicts don't target your creatures but you and wrath doesn't target at all.