I don't have teenagers myself and I also came from a very strict yet dysfunctional home.

I was given some advice in one of the courses I did while working with teenagers though and it sounded like good advice to me (but I haven't tried it out). The advice was to say yes to teenagers as much as possible but put the responsibility on them to meet the conditions. For example, asking to go to a party or the mall, answer along the lines of 'Yes, but you need to ensure that someone's parents are there, there is no alcohol involved and that you are home by 12' or whatever conditions you think are suitable. Instead of asking the questions before giving permission, such as "Are xyz's parents going to be there? Is there going to be alcohol?" etc, you throw the ball in their court to figure out what to do. It gives them responsibility, shows trust in them and means that you get to say yes more often. It also means that if it doesn't work out, you aren't the bad guy who says no, it is their responsibility to make sure the conditions are met if that makes sense.

Don't know if that is helpful at all, but it sounded like good advice at the time.