"Rikudou no jutsu" is the japanese, generic term for the six paths abilities. You should learn the names.
Gakidō -> Preta Path
Chikushōdō -> Animal Path
Gedō -> Outer Path
Jigokudō -> Naraka Path
Ningendō -> Human Path
Shuradō -> Asura Path
Tendō -> Deva Path
I know these names as the six paths of reincarnation. That's the japanese generic term for them, the paths to enlightenment. Six path abilities or six path justus, not so much the same exact thing. I remember Konan and Naruto dubbing these paths as the six paths of pain.
And Madara showed Gakidō (chakra-absorbtion), Tendō (Chibaku Tensei, Tengai Shinsei) and the black chakra rods that are also linked to the Rinnegan. Sasuke showed the same paths and Kurama said that he learned to use the six paths techniques (Rikudou no Jutsu) in the fight of VOTE2.
Madara showcased absoprtion, I know that for sure. I'm yet to read where you got Tengai Shinsei being anything of that from Deva path. The last time I heard that name was from a naruto game not the manga or anime.
I would never count in black rods as being a rinnegan thing considering that both Kaguya, black zetsu, and the Shell Gedo mazou were able to produce those receivers despite the lack of a rinnegan.
Sasuke never showed any paths as much as madara didn't.
All Sasuke did was use amatersu/blaze control, chidori moves, Susanoo, justu absorption, chibakui tensei, genjustu, and rinnegan swap justu. I'm yet to see this "rikudou justu" you speak of. Do you have a manga page or an anime image of it?
First of all, Rinnegan is not Sharingan, so the rules don't apply. And besides that, Sasuke got Itachis eyes but he did NOT get Itachis mangekyou sharingan. If that was the case, then he would have Itachis MS-pattern, but he created a new, mixed pattern.
The sharingan became the rinnegan and what set of "rules" did you come by to set this conclusion of yours? Sasuke's Eternal mangekyo sharingan did have Itachi's MS pattern within his formal MS pattern by the way. It didn't change the whole tomoes completely, it just combined.
]Nagato couldn't use Limbo and Tengai Shinsei because he is not the original user of the eyes.
Madara taught Obito the six paths techniques before he died, how would he do that if he didn't have them himself? You can't teach skills that you don't possess yourself.
Where are you getting this original eye theory from? Because if that's the case, madara shouldn't have any of nagato's six pain justus because he's not the original owner. Madara taught Obito what? Madara never had a rinnegan when he met Obito and neither did Obito, so who is teaching who with no rinnegan available?