I have a timber retaining wall about 4 feet tall builting with 6x6 which is leaning probably due to the downspout draining inside. I'm wondering if using an earth auger to relieve some of the pressure and then using a sledge hammer to knock it back straight would work?
That is not unusual in our neighborhood. A sledge will do nothing but break wood. Repairs that have worked are to dig out soil behind the tipped area and replace the vertical posts with longer ( deeper) ones. The larger the concrete "footing" for the vertical posts , the more resistance to tipping. Additional support can be added by driving metal bars into the ground a few feet behind the wall and attach these with steel cables to the vertical posts. The bars and cables will be under the ground surface so not seen , Yes, they will corrode in a few years but by then the soil will have settled down and be stable ( hopefully). I did this with 3/8" steel cable and it was still holding when I moved 5 years later. The digging sounds worse than it is , or contract it.You only need to remove a narrow trench like 2 ft wide and not necessarily all the way to the bottom. An Auger would be a help. I have also seen a new stronger wall built where boundaries permit ; then fill in the narrow gap between the original wall and new wall .