In the anime, during the fight between Itachi and Kisame vs Kakashi, Itachi tells Kakashi that he cannot use his Sharingan as much as an Uchiha can, as he does not possess Uchiha blood. How can Orochimaru use his techniques when his soul is inside another body which possesses blood different to his blood?
I might not able able to cite proof of this answer in all instances, but from what I could gather these (Kakashi's sharingan and Oorochimaru's body transfers) are two entirely different instances. Spoilers alert! :)
In case of Kakashi:
- On Kakashi implying that could awaken his Mangekyo sharingan (chapter 257), Itachi in astonishment credits his genius. Kakashi would still have the inability to use the Sharingan over a long period of time or to full extent of its power owing to the lack of chakra.
- Kakashi does not have the liberty to switch to normal vision like the other Uchihas could do, instead he covers up his Sharingan eye to prevent it from sucking him dry off his chakra.
Adding more to the previous point is that Kakashi despite being a jounin of exceptional caliber does not have a great amount of chakra in comparison to his compatriots or foes. This might perhaps be attributed to his clan (though other than Kakashi and his late father the Konoha whitefang not much is known if Kakashi belongs to a specific clan like the Sarutobi/Senjuu/Uchiha). This is brought into light on multiple occasions such as:
a. His fatigue after fighting Zabusa the first time in the water country arc saying he used the Sharingan too much.
b. When he fights Pein and uses a ligtning clone where Akimichi Choza wonders aloud how much chakra kakashi has left.
c. When Kakashi explains to Nara Shikaku about how greatly his Kamui's (power of his mangekyo to create a portal and suck objects into a different dimension) ability could be used with Naruto/Kyuubi chakra for massive teleportations such as swapping himself or Naruto in comparison to being done with his own like the case with Deidara where he could barely absorb his hand after a very long preparation.
In case of Oorochimaru:
Oorochimaru does not appear to have any visible bloodline limits on his own. What mostly has been observed until now is a normal summoning of a giant snake (Manda), ability to use a bunch of snakes shooting out from his arm to grapple victims and in some cases moult out of a body (a new Oorochimaru comes through the mouth of the current one which becomes like a shriveled snake skin) and a brief multi-headed hydra like form which Itachi makes short work of.
From what we know these might not be bloodline limits at all, merely forbidden jutsus or a result of his self-experiments. In one case Sasuke in his cursed seal transformation uses a bundle of snakes when Itachi chops off one of his wings during their fight.
Oorochimaru 'takes over' the body of the host that he wishes to use (more of a parasite like characteristic). Hence he would only posses complete control over someone else's body (which has the bloodline limit in it) and use it. In one of the episode (a filler if I remember it right) a potential victim tries to resist from his mind being taken over but finally gives in to one of Oorochimaru's promises.
Hence in a nutshell while Kakashi's use of Sharingan is restricted to that of a ninja tool restricted by his own chakra capacity, Oorochimaru is free to explore the limits of abilities of the shinobi whose body he takes over. Hope this helps.