Pointers from Hyun!
-> First of all, easing is not the root of your problem because you do have easing in there, maybe add a little more, but it's still pretty fine.
-> Instead, work on adding more frames to your animation especially at the turn-around because you'll see that he turns around in only about 2 frames. Pay close attention to his legs and how it bends. Stick animation is 2-D, but there is also depth and 3-D involved.
-> Watch the planting of the feet also. On the onion skin, you need to make sure the feet are perfectly on the same spot or else in each frame it'll slowly start to glide in a direction without you noticing.
-> For the wobblies, you can fix that by zooming in more when you animate and using the max brush size.