The problem is that the bone strengths are affecting the whole character, if you are working with bone strengths i'll recommend you to use the flexi binding feature.
I did it for you: (still needs fixing i just added the flexi binding)
https://www.dropbox.com/s/5t710vfs1jl3h ... .anme?dl=0
If you are working with points (bind points) well... there are many techniques for this, but if you want good deformations you have to use smart-bones to fix them.
You are also getting some weird deformations in your animation because of the way you are moving(translating) the bones. (you should only rotate them, unless you know exactly what you are doing)
You can find some very useful tutorials here:
http://anime.smithmicro.com/tutorials.html