The level of power displayed in the Tenchi OVAs always seemed, I thought, to tap in nicely to U_K's system of divinity, albeit not perfectly.
The Light Hawk Wings that Tenchi uses basically convert any matter they hit into energy; this goes for the whole of the object hit. Kagato was slashed across the chest, and completely disintegrated (I think we can agree that that term is close enough).
Given what the series tells us (possible spoilers here for the third OVA series), Tenchi himself is in fact the Supreme Being; in nascent form, at least. His ability to generate Light Hawk Wings is thus an Esoteric Ability (though it's far more than one strata removed). It's worth noting that killing him essentially just forces him to manifest as the Supreme Being completely.
Z, by contrast, was a much higher divine rank than mortal-Tenchi, and had the ability to generate Light Hawk Wings as a properly-purchased divine ability, hence why he has more of them (and more knowledge of them) than mortal-Tenchi. He also somewhat answers the question of what happens when two people with Light Hawk Wings fight; Z simply nullifies all three of Tenchi's LHW's at the cost of his own, leaving Tenchi with none and himself with two.
Given that Z is clearly less powerful than the Choushin, but still able to defy them, he's at least of sidereal level (though he doesn't have the pantheistic tie to a section of reality that U_K's sidereals have - note, however, that D3 and the other guardians of the dimensions do).
Given God-Tenchi's power level and Z's power level, this would seem to pretty clearly place the Choushin as being Eternals. Precisely what level of Eternal is hard to figure out, as they don't have any characteristics of needing to complete themselves by consuming sidereals the way Demiurges do, and likewise U_K's rules for Time/High Lords seems to lean heavily towards one such being for a particular universe (the Choushin, by contrast, are three sisters who are creating multiverses because they are actively seeking out the Supreme Being; they do this because they have perfect knowledge but still don't understand how they came to exist).
So what level does that place the LHW's at? Well, if Tsunami is an Eternal and can use ten of them, and Z is a Sidereal and can use five, and Tenchi is a mortal (or maybe has a divine level that is less than a demigod) who can use three (at least six after the first time he's awoken as God-Tenchi), then - presuming Tenchi is a special case - they must be a Transcendant ability, which would mean that in fact, Z is also using them as an Esoteric Ability (more in line with the normal rules for doing so).
Regarding the LHW's power level, they actually vary quite a bit in the series. One of the Tenchi novels does say that conventional power could pierce one, but it'd take "a reactor the size of a planet" to generate enough energy to do so. Also, remember in episode five of the OVA series, Tenchi has Ryu-Oh (a second-generation ship) throw it's LHW's at the Soja (Kagato's ship), which fires it's own world-destroying beam in response. The LHW's are actually overcome, and the much-reduced beam destroys Ryu-Oh.
Presumably, the Counteractor can also overcome the LHW's (whenever Tokimi - one of the Choushin - manifests her power in the physical universe from the higher dimensions, it creates an opposing energy elsewhere; the more she uses her power in the universe, the stronger this opposing energy grows. This is called the Counteractor, currently in the form of Lady Misaki, one of the queens of the galactic Jurai Empire).
