For me, I get off shots a lot quicker on the off wing because I can simply snap the puck off in stride instead of having to come across my body when coming down the right side. And as you play more and more you figure out that the key to scoring is not being able to pick corners, but to quickly get the puck on net before the D and the G get a chance to set up for it. A quick snapshot (quarter of a second release) just thrown at the net, in stride with good velocity has a much better chance of finding twine than a sweep wrister labeled for top corner. The latter shot is better and more accurate, but the snapper will not allow the goalie time to be ready for it. So playing my off wing, I can get my snapshot off a lot quicker, which is a plus.
Same goes for passing the puck, playing the off side, I am naturally facing all the other players on the ice, so it is a lot easier for me to see openings, and hit them quickly, as once again, you dont have to come across your body with the stick to make a pass, you can just snap one off.
All this being said, it takes some learning because you have to get used to playing with your backhand, a lot. Catching passes on the backhand softly and controlling them is not easy, and it took me quite a long time to be able to do quickly. If you cant catch the puck, the above benefits are of little use. You will be using your backhand to catch the majority of off wing passes, and it is difficult to learn to cradle the puck on the part of your stick with no cradle.
Defensively, it is much more of a challenge to play off wing. Your back will be to the play a lot, and it is harder to chip pucks out of the zone. Much the opposite of your offensive zone play, you will have to come across your body to get pucks out via the boards on D, and skating/passing the puck up through the middle of the ice in the D zone is much more risky than going the board route.
In conclusion, the off wing does offer some tangible offensive benefits, but until you master the fundamentals of the game (to your level of play, no need to be a D1 player in a D4 league) like catching passes, chipping pucks out of the zone, being in good position, stay in your strong wing and worry about your complete game first. If you put in enough work, you will eventually be able to play off wing and reap the offensive rewards in a short amount of time. Face it 90% of us on this forum are not pro level players with undeniable natural born talent. For guys like us, being able to execute different things is just about repetition and memorization. So if you just work at it, youll get it pretty quickly.