Question

What is the order of weakest to strongest connotation of ( strong, capable, mighty)

Answer 1

The order is capable, strong, then mighty.

Answer 2

The actual classification is very difficult. 
Strong is very open ended. You can be physically strong, but morally corrupt. 
Capable suggests a skill that is above adequate. You can be a warrior that is capable but he couldn't add two single digit numbers together. 
Mighty has the same problem. 

I would pick capable, strong, and mighty