So regardless of whether you meet with her father or meet with lady singh, you'll have a chance to get with Oriana. When in the subway looking for her after Emily contacts you, make sure you choose "Move On", not "Investigate". After she wakes up "Promise to protect her". When she mentions wasting your time after trying to meet the fire elementals, tell her "We didn't". On day 34 you'll find her collapsed in her apartment, you'll stay the night only if you chose the 3 options I mentioned above and have enough points. In the morning of Day 35 ask her "What is it".
At this point assuming you did what's above, you should have sex with her. It's important to make these choices, if you don't you won't have enough points with her and she may have a variable that makes her antagonistic towards you (specifically you HAVE to promise to protect her to avoid the bad variable). I believe you can get an extra point by meeting with her father instead of Lady Singh, but you'll miss out on the chance to get the Rakshasa as allies. Either way you end up with Oriana as an ally if you make good decisions. It's worth mentioning that all of this is except for the choice between her father and Singh is marked by the Walkthrough.
As far as I know there aren't any other variables that influence her scene. Also, I normally go with Lady Singh, so this MIGHT play out different for someone that goes with her father, but as far as I can remember it plays at more or less the same, her dialogue just changes.
