Camden defended doggedly but further strikes from Leor Sidle, an own goal and super-sub Jonny Quinn sealing the points.
Oakwood forged ahead midway through the first half with a brilliant strike from Levy from the edge of the box.
Sidle doubled Oakwood's advantage with a close-range tap-in following a goal-mouth scramble.
The visitors were gifted a third in comical fashion via an own goal before super-sub Quinn completed the scoring.
Oakwood joint-manager Dan Kristall told JC Sport: "It was a good win against an in-form Camden side.
"Ultimately, we had too much quality, power and pace for them and scored some nice goals although we were quite wasteful for an hour - mainly due to our decision-making and finishing, and we know that this could hurt us in the weeks to come.
"Fair play to Stirling and his Camden side who defended well for an hour. We wish them well until we next meet them in the league.
"They have enough battling qualities to stay in the division and have already beaten a few good teams this season.
"As for us, we take the positives from this one, work on a few things and go one game at a time, focusing all of our efforts into a huge game with Hendon on Sunday."
Camden boss Stirling Kay told JC Sport: "We were in the game until 60 minutes after falling behind to a great strike from out side the box.
"We managed to stop them getting behind us and Oakwood had very few chances in the first half, and were getting very frustrated.
"We were getting more of the ball in the last 15 minutes but we then lost two forwards to injury, so our threat to attack Oakwood was at a minimal which left us with very little cutting edge.
"We worked very hard in the second half but unfortunately they scored three goals, including a wonderful flying header from Josh Tiano, but into the wrong net!
"We all felt that if we have more attacking options we could’ve made it a far closer game. Defensively we we were very good. But we have to do much better in the last third."