MVP, we totally understand that you have a bunch of things going on and it is not easy to juggle a number of things at once. But you can lose 15-20 pounds in the next 3-4 months by just making a handful of adjustments. Adding cardio is obviously helpful but it needs to be in concert with a well thought out diet plan.
You should definitely re-evaluate your diet if you don't feel it is working for you but don't completely toss the weight loss goal out the window for the sake of your health if nothing else.
I am no nutritional expert so I won't pretend to know how to go about losing weight so all I can add is my best wishes and hope you achieve what you set out to. The lads here have already given some good advice.
P.S I used to love soft drinks too. Actually find that Pepsi Max is not that bad