First off - 20 lbs is great! It sounds like you have gotten into a great routine for cardio exercise, but it sounds like you have hit a plateau. Strength training, while it probably won't have any quick effects on your weight loss, it may be what your body is looking for to break the plateau. I believe the science is that, the stronger a muscle is, the more effectively it operates and burns more calories doing the things you already do.
When I started doing serious strength training with a trainer, the number on the scale didn't drop, but the shape of my body started changing pretty drastically. I lost inches from places I had always loathed. It also made the cardio much easier to do.
As far as diet goes....I have never done it, but I know that friends who have followed a "Paleo" diet have seen some pretty good results right off the bat, as far as straight weight loss is concerned.