Good to fly?

See if you agree.

KHEF 131446Z AUTO 33014G18KT 3SM OVC013 07/06 A3015 RMK AO1

Class B,D and E airspace restrictions for VFR conditions (HEF, IAD, and beyond)
3 statute miles? YES
500 feet below? Lowest clould cover is 1300 AGL, so maintain below 800 and 500 ft about sparesly populated areas/structures/persons. It is not comfortable but legal. Just note that a 1000 AGL and 2000 Ft avoidance it required in congested areas.
1,000 feet above? Not getting there without flying through clouds.
2,000 feet horizontal? Not getting there without flying through clouds.

So, heading west, avoiding the town of Manassas, seems doable but provides a narrow range of safety since mountains are nearby as well as pockets of congested areas. Exceeds my level of comfort.

What about that wind? Well, I believe my POH (Cessna 172 N (I believe....I should know!!)) states not flying winds that exceed a 13KT crosswind. With gusts of up to 18KT, I would not fly.

Now what about that ADIZ? I have not currently found anything concerning altitude minimums that differ within the ADIZ. When flying out, the selected altitude has been about 025 and 022 on the return, neither of which can be met in this weather condition.