If memory serves me correctly, the terms left and right in respect to politics came about as a result of the French Revolution. I don't know the names and specifics, but supporters on one side were more radical in the sense of wanting to change the status quo (the left) while those on the right were more intent on holding to the French constitution, etc. It was all relative to where whomever was sitting. The terms just stuck with us after that.
There are numerous verses in the Bible where it says not to swerve too far to the right or left (paraphrasing). Deuteronomy 5:32 is one such example.
Veteran, I don't know that the right hand was so much associated with righteousness, as it was power. The right hand was the average person's dominant hand. Lefties were considered weird and even evil by some cultures (sorry lefties). I remember eating with my left hand one time as a young child, and I was asked why I was doing that. I cannot recall if it was my great grandmother or grandmother, but the left-hand was viewed superstitiously for a long time.