No. Quite a while back, a dev confirmed that no enemies had specific weaknesses, except for Devidians to Proton damage (not antiproton), which only comes from a single special weapon. Admittedly, Tholians and Elachi are new after that, but there's no evidence they're any different.
Some factions (like Borg) do have elevated resistances across the board, and it's not always equal between kinetic and energy (Crystalline Entity has higher energy resist than kinetic), or shields and health (ground Elachi have very strong shields and very weak health). Borg also have a particular resistance to phaser and polaron procs - not the damage itself, but you do get reduced milage from the secondary effects.
Certain weapons can make certain enemies easier to deal, with take the Elachi they have crazy high strength shields, so minor brainstorm what if I used the Borg prosthetic - Maintenance Drone Mk X [CritH]x2 since the secondary fire is a shield neutralizer and primary fire is plasma which several members of my away team get a bonus to plasma damage. Long story short I picked up 2 the other day while running defera and my team slaughtered 'em mwhahaha. big Elachi bosses with crazy shields not anymore between those and the 2 engineers on the away team running Chroniton mine barrier it was a cake walk. one problem I had was those silly skittering facehuggers, but I'm thinking I want one of those as a combat pet now
Some of your opponents do have weaknesses on the ground.
Tholians are susceptible to vibrations; the sonic [sonic] weapon bonus is very effective. Sonic capable weapons come from reward bonuses on Nukara. There are also affected by cryo or cold weapons. The breen weapons that are rewards from the Breen series are partially effective.
Elachi are susceptible to mental attacks; no weapons bonus but a Reman or Lethian player can use a mind attack to great effect. Also the Ophidian cane has proven to be quite useful.
Borg used to be susceptible to the [borg] weapon 'radiation'; this is no longer the case. Melee has proven to be effective against them, if the player is properly kitted out.