TL;DR

Hydra for lane dominance vs squishies and bruisers.

Black cleaver vs mega tanks as a third item at best.

Trinity force when you're going for speedy gonzales to keep sticking to your target. But if you really wanna stick to your target, a Frozen mallet would also be a good choice for the tank stats + Passive it has. Same being slightly cheaper, though the damage will be slightly lacking.

Still don't see a reason to give the Hydra up. Scales very well with him aswell.

Numbers:

6% per stack on his passive per second.
Up to a 150% of your bonus AD at full stacks.

70% to 105% depending on the zone you hit your opponent in.

20% to 100% extra damage depending on what level the W is.

E has none...

R has a 75% to 150% of his bonus AD.

Not to mention the active it gives.

Now for some math:

Passive will deal an extra 4.5 per second per stack. (that's 22.5 on one stack to 112.5 damage when fully stacked)

Q will deal an extra 52.5 damage to 78.25 damage.

W will deal an extra 15 to 75 damage depending on rank.

R will deal an extra 56.25 to 112.5 bonus damage.

That's a shit ton of damage added if you ask me. The potential is limitless.

Tri force is best suited for longer skirmishes, where Darius favor short bursts vs squishies. Or kiting/chasing. So the math won't be done on it since it has the strengths on it's own.

Black cleaver however is an item that is best suitable when facing a hypertank in the toplane. See Malphite, Maokai or Mundo.

That is when you want the Black cleaver, but favorably as a second item or third and act as a frontline buster.

So what is the strengths of Hydra?

Well, if you already snowball, you will snowball much harder. That's for sure. The added damage from the active and the stats really does reap up a reward fast and lets you punish every misstep harder from the opponent.
It's also cheap for the powerspike it gives. Really ruthless. :P