Your overall feel for the water will improve as you work on new pathways of the hands when attempting the other strokes. The risk of overuse injuries will also reduce as the new movements from the other strokes redistribute the workload of the arms and shoulders.
At the very least, adding backstroke to your swimming would be a great addition to your stroke repertoire. Backstroke is a natural stroke to use to help unwind the shoulders from the vast amounts of freestyle we swim as triathletes. It also helps build aerobic fitness, which is very useful if you are still getting the timing and breathing patterns in place on your freestyle. Try swimming alternate 25m lengths within a 200 as freestyle and backstroke to generate a natural fartlek swim, which will allow you to relax a little more on the freestyle while naturally working a little harder on the backstroke. This is because the kick and core work is greater during backstroke because of increased drag due to the position of the head and lunges compared to freestyle.
For a few years now we have been incorporating other strokes to our triathlon fitness swim sessions for those at the right stage of their swimming. These medley alternates are promoted as a kind of cross training, which has helped our swimmers come on to the idea very quickly. The following video is a rundown of drills derived from the other strokes, which you can do without having to completely learn the other stroke and still receive the benefits to your freestyle.
Breastroke arms with freestyle kick: This is a nice variation for practicing a continuous leg kick. The first part of a breaststroke pull is also similar to the way we scull the hand into the freestyle catch. It is optional to wear fins, but it can help with your kick.
Double-arm backstroke with a pull buoy: A great way to stretch the shoulders and chest muscles through a different range of motion after a lot of freestyle.
Freestyle arms with butterfly kick (we call it tri-fly): A tough one to perfect because it takes a lot of concentration to master the timing and coordination.
All these strokes combined in an Olympic race is known as the individual medley. This pool event has been made famous by the duals between Michael Phelps and Ryan Lochte. It follows the order of butterfly, backstroke, breaststroke and finally finishes with freestyle. The 400m individual medley is perhaps the hardest pool event due to the positioning of the lung-busting underwater breaststroke pullouts on the third 100m.