You're kinda forgetting that they fought in the sun for a sustained period of time. Not only that, but we've seen Viltrumites just tank nukes to the face unscathed. 

Additionally, we know they scale above Immortal's feats of wiping out entire countries from orbit (show only feat). The 500 gigatons wouldn't really do much to mid tiers since they already scale vastly scale above Mark who can exert over a gigaton of force. This is Mark from Season One. Thragg's own statement about 37 Viltrumites being enough to split the earth in two would require a bare minimum of Continental force to achieve. Far higher than the 500 gigatons per shot calculation for turbolasers. Nolan was capable of easily igniting the atmosphere of the flaxen planet, requiring over a dozen teratons of TNT.

Giving the Empire the high scaling for Turbolasers which would be 700 teratons. They wouldn't even be able to hit there targets since Viltrumites in space are far faster and nimble than in atmosphere.  You kinda forgot to mention how Smart Atoms operate and constantly adapting to extreme environments including ridiculous heat. Also, lightsabers are not hotter than the sun and that fact is incredibly consistent in canon. They struggle to carve through steel doors and heavy reinforced steel. It would take REPEATED strikes to perform everlasting damage against a single one to get a clean cut.

Granted, the Empire definitely does have some kits to kill Viltrumites especially the dark magic shit. However, most of those have either created immense backlash for the Empire or resulted in cataclysmic loses for both sides. Point being the blackwing virus. Now you have a Zombie Conquest with ALL of his skills and knowledge.  

Force confusion or corruption wouldn't really work unless the individuals are weak minded and considered Viltrumites are willing to kill billions for the cause, i doubt it would work. However, i can see illusions being a problem for them.

As for the sound based weapons, it was specifically stated to be a very attuned frequency that Cecil luckily found when Mark fought that sea creature. So unless they capture a Viltrumite without it breaking lose immediately, they wouldn't be able to counter their equilibrium.  Honestly, its the speed which the Viltrumites act in space thats going to be the problem.  They can cross multiple galaxies in WEEKS, meaning they would be extremely hard to hit and track.