I would imagine that the goal is to eventually make ALL the melee weapons in the game usable, fun, and effective to use on all difficulties. Each should have its own niche role so as to make the game more interesting. Anyhow, the following are my suggestions for these three underpowered weapons.
War Pick (Bardin) - This weapon is similar to the Exec Sword but I feel that it differs because 1) it is not as good against hordes and 2) its heavy charged attack is even slower but does not do enough dmg to be worth the slower response time and charge speed. My suggestion to make this weapon viable is to increase the dmg of the heavy attack to make it more competitive and worth while. I see almost no one using it in the meta (except for the occasional new player who does not know better).
Two-Handed Sword (Kruber/Saltzpyre) - This weapon is sort of a meme almost right now. It only has cleave type attacks and very little armor piercing so it is worthless against elites. It has only one saving grace, which is its anti-horde crowd control capabilities. However, I think you could strengthen these capabilities to solidify its niche role in the meta and make it worth the trade-off of not being able to fight elites with it. Perhaps increase cleave, stagger, and maybe even increase the armor piercing ratio a little for the heavy attack. It should be much better against hordes than the Exec sword so as to make it worth using over the latter.
Two-Handed Axe (Bardin) - This weapon certainly has its place in the meta but most would call it mediocre. It is strong vs. Elites but not as strong as other 1H weapons that can more reliably score headshots. It has better crowd control capabilities than these 1H weapons but is not as good at cleaving through hordes as compared to other 2H weapons (e.g., 2H hammer). Anyhow, I think one complaint that people have is that it this weapon has a very slow reaction time when it comes to quick blocks. So if one is attacking and turns around to quickly block an attacking foe, they will not be able to cancel their own attack in time and block. It makes it difficult to block with it and therefore, other weapons are more attractive. I think improving that block time reaction would make this weapon more usable in the meta (Legend).