You'll find that you don't need to do all that much work to improve postural muscle strength. Once you get these muscles in shape, it takes very little maintenance to keep them that way.
After a few weeks of diligent strengthening, you'll be more efficient, and your running will feel easier.
When I realized I needed help with my posture about 10 years ago, I did some research and eventually came up with a program of eight to 10 strength exercises.
As I combined or eliminated certain ones over the years in my search for efficiency, I worked my program down to two basic exercises. Call it Jeff Galloway's Posture Program, and you don't have to go to a gym to do it.
To do these, lie on your back with knees bent at about a 90-degree angle. (Doing crunches with legs straight puts too much stress on the lower back.) With each crunch, lift your shoulder blades off the floor without "dropping" your head forward. (Bringing your head forward puts too much strain on the neck and shoulders.)
Go up till your shoulder blades are just a couple of inches off the floor. Come down slowly each time, but not all the way down. Keeping your stomach tight throughout the exercise will really work those abdominals. Try to do crunches every other day, working up to 40 or so per session.
To balance abdominal strength, you need to build up your back and sides, too. A great way to do this is by "arm running" with hand-held weights. (If you don't have dumbbells for this, you can always use water-filled plastic jugs or anything else of appropriate weight that can be grasped.)
To do the exercise, stand erect, hold onto the weights and begin moving your arms as you do during running, while keeping your feet firmly planted. You might want to glance at a mirror while you do this, so you'll be sure to stay in the proper posture. As with running, keep your elbows bent at roughly 90 degrees as you pump your arms. Continue until fatigue sets in. Try to do this exercise every other day.