I think we need to stick to the fact that the heirlooms personify the founders. The diadem increases the users intellect and the sword protects the user from danger. Following this trend we can see that the cup should relate to loyalty, and the locket to cunning.

So what would inspire loyalty. Love is a good motivator, but I think more importantly, loyalty is based on trust, and knowing that the person isn't lying. The cup could require whoever drink from it tell the truth, the first form of veritaserum, maybe not as strong, but instills a need to tell or desire to tell the truth.

The locket on the other hand needs to help the user personify cunning. It could allow the user to become more perceptive of his surrounds, allowing him to see things otherwise lost, giving him an advantage in manipulation. Or it could take the diary's approach and alter the perceptions of people on the user, similar to a vampire's ability to allure and seduce others.

 

The items could have a sort of fairy tale enchantment on them.

The sword, which would be used by a brave knight, is a weapon to help any wielder fight the monsters in the dark.
The diadem, which would be worn by a wise and beautiful queen, is headwear to help her with her tough decisions.
The locket, worn by a lover going to war, will always help the wearer find anything depicted inside.
The cup, used by the devout nun, will always have enough to share with those who need it.

It seems a bit silly, but it weaves in a sort of form-defined use.

 

I always thought the "older it is more powerful it is" was the result of allusions to the difference between the European Dark Ages and the Roman Empire which preceded them?

And, building off the idea that each object personified the Founder, then perhaps the Chalice nullifies any poisons placed within? It doesn't make others more likely to trust the user, but it could be waved away as the other Founder's use of the Chalice showed their trust in Hufflepuff that she wouldn't use the position to betray them. Not anything particularly amazing, but it kind of ties into the idea of cup-bearers being the most trusted members of a royal court.

 

The diadem is said to augment the wearers mental strength/concentration/memories or something like that.

The sword takes magical things(mostly liquid i.e.: basilisk venom ) to strengthen itself.

The cup is tricky. In ffs they always make it like itt will purify any liquid poured in and I agree with it. There is no poison between friends, right? Inconceivable

The ring, well it raises the death, being it is the Resurrection Stone.

The medal, I always thought it was a primitive or low powered pensieve. That is capable of holding 1-2 two memories. that's why you could explain how in DH the shapes came out of it , albeit corrupted to protect it. It could have been given to him from his lover/wife or from Godric in honor of their buttbaby.

 

If the locket was Slytherin's and his skill set involved Legilimency and magical husbandry, it may have imparted some natural affinity with and/or influence over animals.

 

Slytherin's locket could perhaps allow a parselmouth to control snakes even if they are loyal to another master?

And perhaps give an extent of control over people? Like the Snake with Eve in the Bible, Salazar was the master of manipulation after all, kind of a middle ages imperius curse thing

Imagine how the whispering in the mind thing worked in the Goblet of Fire and it could have a similar effect?

 

Maybe Hupplepuff's cup turns water into wine.

 

Salazar Slytherin was supposedly a powerful legilimens, maybe the locket enhances a users mind magic. Maybe you won't need eyecontact to use it anymore. Not only would it be sneaky as a Slytherin, it would also be totally professor X-style. If your in a wheelchair.

The sword and diadem is already stated. Sword being able to absorb what makes it stronger and honestly, it's pretty powerful.

The diadem enhancing your wisdom/making you more intelligent is more or less confirmed as well. To what degrees could be decided by checking the other items powers and having the users intelligence being raised proportionally to their abilities. Making them balanced is rather important after all.

However, I had the idea that the cup could be used in divination.

They do read tea leaves. Maybe Hufflepuff's cup is a powerful divination tool, maybe it allows people without talent to divine or maybe it's more precise than normal methods. It could perhaps even allow one to witness a possible future as long as the future is ever-changing. It would than be helpful, but not completely overpowered as having an answer sheet to life would be.

 

Maybe the cup, when replete with feces, compels no less than two witches in the vicinity to sup from it.

 

I thought a good one for Slytherin's locket would be to grant the wearer limited Parseltongue ability. Not potent enough to speak it at will like Voldemort or Morfin, but closer to Harry's ability, where he can do it by accident or if he concentrates hard enough.

Ever wondered how Ron could get into the Chamber in DH? Slytherin's fuckin' locket.

 

It's more likely that any of the Horcruxes could grant that ability - see, Ginny.