Nani is just as effective on either side of the pitch. He crosses better from the right but he gets more goalscoring opportunities from the left; either way United get about the same volume of end-product from him. His interplay with the fullback is always key; when Evra is on form (was on form) there's no better player to link up with Nani; on the right hand side he links up excellently with Rafael, well with Smalling, but not so much so with Jones; this is why Jones shouldn't be played as RB behind Nani.
Nani's reliance on a fullback who understands him is so much more exaggerated than that of a winger such as Valencia, because unlike the latter Nani plays much of his possession game standing still. Valencia beats his man with raw pace and power, he'll often sprint so far ahead of play that his compatriot fullback's role will become more or less redundant as an attacking option, this is what's works for Valencia and he does it to great effect. Nani though relies on his fullback much more to work his way up the pitch, interchanging positions with him, overlapping and knocking balls too one another looking for the correct opening with space to run into; Nani will often stop the ball dead and lock his opposing defender in place who won't be able to make a challenge due to Nani's much quicker feet; it's at moments like this that Nani's teammate comes into play, either offering support so Nani cab make a run or making the overlapping run himself so Nani can play the through-ball. This is something both Evra and Rafael excel at, but something Phil Jones doesn't do very well. Compare such interplay in a dead-stop situation with Valencia's game and you'll see that the Ecuadorian uses the fullback far less; his acceleration is much better than Nani's and so he's much more likely to attempt to beat the defender on his own accord.
Either side then, left or right, Nani can be just as effective, which grants the luxury through this versatility of being able to just fit him in where he's most needed. The form of Ashley Young, Valencia and Evra and the fitness of Rafael and Smalling will all come into play when deciding which side of the pitch, if any, to position Nani. If Evra's is going through a bad patch and only Jones is available at RB then Nani probably won't play, this because Ashley Young can better play ahead of an underperforming Evra than can Nani and Valencia can be just as effective ahead of Jones as he'd likely be with Smalling or Rafael.