For starters, in a song, you will want to keep to the rhythm, the meter of the song. So that might be one reason to use righteous instead of right.
Then, righteous and right are related, righteous being descriptive of someone that does the right things. The right side of hell might not be the same as the place in hell were the righteous people are, but that might lead to a more theological or philosophical discussion than would be appropriate on this site :)
As for the "wrong" equivalent, you might be looking for "wicked" - it is often used as an antonym for righteous.