Or am I just using them wrong?
I see no situation in which a pathetically weak Leviathan Blade with a UV for high damage bonus vs undead can be better than a standard Leviathan Blade or a Normal/Elemental damage weapon. It just has no versatility. If you keep one on-hand exclusively for use against undead enemies, you could easily fulfil that purpose with one of the 5* Brandish weapons or an Avenger. If you use it as your main weapon, a Leviathan Blade is honestly more useful, has greater versatility, and does better in general than a Vanquisher except when up against the undead. The Vanquisher does nothing better than any other blade, and is in fact weaker than its rival blade against all enemy types except undead, which other blades already do better.
The Iron Slug is also weak. The Valiance does better damage faster, and doesn't require the player to stand still. The charge attack is also much more useful. It also loses its ability to Stun except with a charge attack, either that or it's just exceedingly rare for the stun to proc compared to a Mega Magnus. This weapon is almost a downgrade from the Mega Magnus, with the only bonus being that its damage type changes to the universal "Normal" damage type, something that the Valiance already covers much more efficiently and with far less movement penalty.
So I don't get it.
Are they underpowered, or am I doing something wrong here?
They may be weaker than other weapons but that doesn't mean they're underpowered.
They're only underpowered comparatively.