The orcs have not been hit by a melee weapon attack
Slashing Flourish:
You can expend one use of your Bardic Inspiration to cause the weapon to deal extra damage to the target you hit and to any other creature of your choice that you can see within 5 feet of you.
All of the creatures1 of your choice are taking damage, but what is dealing the damage? "The weapon" is dealing the damage. It is dealing damage to both "the target you hit" and to other creatures (that you did not hit).
Wrathful Smite:
The next time you hit with a melee weapon attack during this spell's duration, your attack deals an extra 1d6 psychic damage.
Who takes damage from the smite? The target you "hit with the melee weapon attack". What is dealing this damage? "Your attack". The ogre has been hit by a melee weapon attack, but you have not hit the orcs with a melee weapon attack. They have been damaged by your weapon through your slashing flourish, but they were never targets of an attack, and were not hit by the attack, because you did not make attack rolls against them.
If there's ever any question whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack.
Despite this "simple rule", there are instances in which you are making an attack without making an attack roll; grappling and shoving, for example. The consensus, on this site at least, is that something is an attack only if it includes an attack roll or if its text clearly indicates that it is an attack. Slashing flourish does neither; it is a source of damage but is not, in itself, an attack.
Does the sword hit all of them?
No, the sword damages all of them, but it hits only the ogre.
Who gets psychic damage?
Only the ogre.
Who makes Wisdom Saving rolls?
Only the ogre, and, arguably, only if it chooses to, since it "can" (not "must") make a save.
Who is frightened?
Only the ogre, and only if it fails to save (or, arguably, chooses not to attempt the save).
1 Note that the ability says "any other creature" of your choice - not "all other creatures of your choice" or "each other creature of your choice". Nonetheless, the intent seems to be that it can, in fact, be applied to multiple creatures.