As much as your current situation is terrible, I would never quit without a new position lined up. I've seen a number of people do it and it set them back years - they struggled to find a new job and as their desperation increased, they were forced to accept a lower position with lower wages.

If you interview for a new position while still employed, you are in a position of strength (as much as I hate to put it in those terms). If you interview while unemployed, you're likely to NEED the job and potential employers know that - this will inevitably affect your bargaining position.