Does Diffusion Sliver protect from boardwipe spells and sacrifice spells?
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:


Twiddle would target the Sliver and trigger this ability. 
Turnabout wouldn't, because the card doesn't target a creature, it targets a player. 
Call to Glory would not target the Sliver, as it doesn't target anything.