I'm sure you've heard about this technique, often used by writers, of conducting impromptu interviews with characters in order to get to know them better. I've written posts suggesting questions for such interviews myself (like here).
Answering questions like these will often provide you with useful information about your character. If you've asked the right questions, this information can help your story a lot. However, a simple interview format has one large disadvantage:
It isn't good at capturing how the character would think and talk about him/herself.
I've tried to alter the questions I use to improve my results in this regard, but the real problem isn't the questions. The problem is the questioner. Think about it this way: would you talk about your life and your concerns in the same way to yourself, or your spouse/best friend, as you would to someone who came from a foreign country? Of course not.
However, when you ask questions of a character who resides in a world not our own, the answers you are likely to get are those you might give to someone from a foreign country or another world. You'll discover that all kinds of distance markers start creeping in - names that you'd never use, ways of defining oneself that we never think about unless dealing with outsiders.
How can you defeat that tendency so that you'll learn more about what your character should sound like on the inside? It's definitely a challenge. In the post I linked to above, I have a list of eleven questions that I've deliberately tried to phrase in a way that encourages you to use your character's voice to answer. Another thing I'd suggest is interviewing yourself, or having a spouse or close friend interview you. If you find yourselves laughing at the questions because you both know the answers, that's a good indicator of shared knowledge that insiders wouldn't bother to mention. If you don't feel you can do an interview without becoming more distant than you should, try looking into a diary that you've written, or letters that you've composed to someone you know well. Look at how you describe your setting and social situation. Look at what you label (group membership) and don't label. How much of it would an alien or outsider really understand? I'll bet you any money that you don't find anything resembling the phrase "Americans do this/believe this because..."
After your interview or research is over and after you have a draft of your narrative voice, try to edit it with an eye for distance markers. These include "Americans" or "Californians" or "noblemen" or anything people use to describe themselves to outsiders. Look for places when you've used "there" instead of "here," "they" instead of "we." Think about what information is normal and what stands out, what is important to your character and what is beneath notice. Make sure you've used "the" to refer to objects or concepts the character knows or has perceived before, and "a" for new information.
Getting into a character's head is a very valuable point of view technique, but the interviews that you conduct are limited by the fact that your character lives in the world you've created, and you don't. Since your subconscious knows that you don't live in this place, I'd encourage you to experiment with an "insider interview" approach or a diary approach to see how you talk about your own world - and then see if you can apply what you've learned to the worlds you're creating.