First, here are expressions for different wiggles:

Uniform scale wiggle:

w = wiggle(5,30); [w[0],w[0]]

Separate axes wiggle:

Wiggle X Only: [wiggle(5,30)[0],value[1]] Wiggle Y Only: [value[0],wiggle(5,30)[1]]

Wiggle X and Y separately:

[wiggle(5,30)[0],wiggle(20,30)[1]]

And here are expressions for Jelly Wiggle:

The main part is the “Wrap”-Effect

Use this expression for the Horizontal Distortion:

warp =effect("Warp")("Horizontal Distortion"); 
decay = .96; 
end= 0; 
duration = thisComp.frameDuration; 
current = Math.round(time / duration); 
amount = 10; 
for (f = 1; f <= current; f++)
{ difference = warp - end; 
amount = (amount - difference) * decay; warp+= amount; 
} 
warp

And this is for the Vertical Distortion

warp =effect("Warp")("Vertical Distortion"); decay = .97; end=0; duration = thisComp.frameDuration; current = Math.round(time / duration); amount = 10; for (f = 1; f <= current; f++){ difference = warp - end; amount = (amount - difference) * decay; warp+= amount; } warp

by Ewan Smith on ae.tutsplus.com

For dynamic wobbly boxes, there are free preset:

https://aescripts.com/wobblebox/