[RPG] If a Warlock’s “Repelling Blast” hits an enethe engaged with an ally, does that ally get an attack of opportunity from it moving away?

Each PC refers to the Opportunity Attack rules.

You [PC] can make an opportunity attack when a hostile creature you can see moves out of your reach. (PHB p.195, "Melee Attacks," at "Opportunity Attacks.")

So, each of your PCs who have not used up their reaction and who can see the fleeing NPC get to make the decision: "shall I OA or not?"

Your Druid Gets Attacked, then the barbarian gets pushed

The trigger for your readied action was:

Cast Eldritch Blast (with Repelling Blast invocation) on the berserker in question if he attacks the druid.

It is stated in the Dungeon Master's Guide (p. 252) that:

If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action.

So your readied Eldritch Blast will occur right after the berserker attacks the druid.

What if, rather, the trigger was the druid moving? What if the trigger was the berserker raising his weapon or rearing back in preparation for an attack?

The alternative triggers would not improve matters much. If you specified the trigger was "the berserker raises his weapon to attack", that might be tricky, because the trigger has to be a "percievable circumstance." In combat, everyone always looks like they're just about to attack each other: what if the enemy doesn't "raise" a weapon, but stabs with it? What if they raise a weapon in salute?

If the tirgger was the Druid's movement, that's no good either because the Barbarian will attack before the Druid moves away from his reach (as that's the timing specified in Opportunity Attacks), and you'd Eldritch Blast after the Druid finished moving away from his reach (since it's a Readied action, and happens after its trigger), so the berserker would still attack first.

A relevant question that has been asked before is can I specify a trigger to be "before... occurs"? (Mostly, you can't).