I just finished an animated character dancing (still waiting to hear, it was a contest, yikes!) and I used Dan’s “Animating a Walk Cycle” for stitching a character together. There’s some great stuff in that tut (Click Dan’s head at the top then scroll down to the tut) about looping, to keep a walk cycle going.
Dan has a cool IK setup here:
https://www.motionscript.com/expressions-lab-ae65/ik.html
Anyway to answer you original question, Distort > CC Bender and Turbulent Displace do what you want, but there’s a glitch if you use Dan’s method (like I did) of parenting for the rest of the body, Bender moves the neck, spinal cord, as you’d like, but it messes up in that the head will stay where it was (since it’s anchor point doesn’t know about bender changing things below). Simple Solution, Precompose, or drag that comp into a new comp and apply Bender(or other effect) to the whole body, and by moving the Top And Base, you can only bend the parts you want, and everyone else stays connected. You can do some amazing smooth body movements this way. You can drag a window out for the other comp so you can see any changes one makes in the other, just drag the tab.
Maybe this will work for you. Good Luck.