I own Kidd, Loyang, Orkan, and Harekaze, so I'll speak on those.
Harekaze first (So you know what you're missing): Kagerou hull, torpedoes, and performance with access to different weapons systems and a flat grey(!) premium camouflage. She has access to six of Akizuki's 100mm guns, three of Midway's 127mm secondary guns, and the basic set of IJN 127mm guns seen on Kagerou. The best option is the 100mm guns, with their increased pen, fast reload, fast traverse, and dual-purpose AA to have at least a small chance of dissuading enemy CVs. She has the option to trade out her smokescreen for a torpedo reload booster, which is actually quite nice to dump 16 torpedoes in the water. Not the best option, unless you really like the Kagerou playstyle or want an IJN DD trainer.
Kidd: A Fletcher with one less set of torpedo tubes, in exchange for existence at T8 and slightly boosted anti-aircraft performance. Her lack of a second torpedo set and abysmal performance on the set she does have (9.2km range, 55 knots, and 2 minutes reload stock) make her five 127mm guns the main way you deal damage with her. To compensate, Kidd has access to a heal, smoke, and speed boost in separate slots. Kidd can also replace her speed boost with DFAA if you're more concerned about the CVs pestering you than you are managing concealment. A decent enough destroyer, and very pretty since she is a Fletcher.
Loyang: A Pan-Asian version of Benson, with standard torpedo armaments and only four 127mm guns. Able to swap her speed boost for DFAA or Hydroacoustic Search, she can be versatile to fight off enemy DDs and screen for your team. Typical of the American DDs, her torpedoes are usable but not reliable, no matter which module you select for them. Loyang is alright, but it is just a Benson in the Pan-Asian tree, and not good for training any captains unless you intend to play through the Pan-Asian line.
Orkan: Polish version of the Lightning-class DD in the Royal Navy's line, but with only one set of torpedoes that are standard fare for the European line (76 knots with 12km range, moderate striking power). Her guns are only 120mm and have a slower reload than the others listed above, but the turrets can traverse a full 360 degrees and lend her to being a very wiggly gunboat. However, her mediocre speed of 35 knots means that most DDs that get within her 5.9km spotting radius will have only slight issues keeping her spotted and remaining undetected. She does, however, get tools to combat this mediocrity: Speed boost, heal, and 7.5km radar all help her in her role as a decisive gunboat, playable similarly to the Soviet DD line (or the rest of the European line, but I never cared to play them much after their initial introduction). If you like to be aggressive, guns firing, slip away and heal, then come back to hammer the enemy more, Orkan is a good enough DD for that work.
As an overall recommendation from this list, Kidd and Loyang are the most workable DDs. They have the options of a smokescreen to disengage from fighting ships without radar, can lay torpedo-minefields, and are able to discourage CVs from staying too long on them (Kidd can even repair some of the BS damage that a CV can do). Harekaze is... just a better DD Akizuki in its best setup, with the ability to launch the two torpedo salvos freely that Akizuki uses her TRB for. Orkan is a nice and aggressive DD, but there's nothing to be done if a CV is continuing to spot and harass you for his team.