Socrates had a peculiar, by our standards, understanding of the world. He believed in the soul (though his understanding was closer to 'character' then our religiously-slanted understanding of it), and believed that we should never do wrong, not because it was intrinsically wrong, but because by doing wrong we harm our soul(s). Additionally, he held that no one could harm another man's soul, that you can only harm your own soul. Below is an excerpt from a dialogue between himself and Crito. In this excerpt he establishes one of his premises for his explanation of why he should not flee the city to avoid execution. I can't get myself to agree with Socrates, that we should never do wrong (understanding wrong as it harms our soul). There is the obvious bit of the greater evil, that sometimes one has to do an evil to prevent an ever greater evil. This is a consequential view, but for me the most important part of it is that Socrates believed that we must not do wrong because it harms our own soul. On some level, I agree with Socrates, that doing wrong harms our own soul, but I disagree with his conclusion that we must not do that which harms our soul. Killing affects sane men, and I agree that it harms their souls, but it is often done for a greater purpose, and that purpose is what justifies it - the harm they take to their soul is a selfless sacrifice. You can read more from the dialogue here
It's a tricky one, because 'wrong' is subjective. But I agree with Socrates in so much as that doing one's own version of 'wrong' is harmful to one's wellbeing. EG: I have absolutely no qualms whatsoever about mocking religion, but would feel bad if I passed a very elderly person in the street without smiling and saying 'good morning'. The former is good for my soul, the latter is bad for my soul. I'm sure there are people who might reverse that.
I think "harming your soul" in this sense means "becoming a bad person." This is why you can only harm your own soul. When it comes to killing people, I don't think Socrates had PTSD or anything like that in mind. Only unjust killing would harm the soul. As far as taking hemlock rather than fleeing, I think Socrates sees two options (1) flee, but sacrifice all of the principles he as fought for, and harm his soul (tarnish his character) in doing so or (2) accept the consequences of the guilty verdict, upholding justice and avoiding any harm to the soul. He picks (2) because he doesn't think principles and justice should be thrown away because they have ill consequences, even death.
As usual, this is just a semantic train wreck. Should we never do wrong? I consider wrong to be the label we put on actions which we should not do, so we should not do wrong by definition. The dialogue given discusses the application of evil as punishment merely as revenge, which I agree with the supposed Socrates on (punishment may deter, rehabilitate, isolate danger and so on, but never be argued from dessert). The act of harming a person in order to stop him from harming a third person may still be considered not a bad thing, and is not really discussed in the dialoge. As you point out, their understanding of soul is more akin to character, which means that an action such as killing a terrorist on his way to kill many people can still be considered good for one's soul, in the same way as many consider soldier to be a responsible profession. What that does to one's psyche, I imagine they did not consider right here, but with the right semantics, it could be argued that breaking a man down psychologically is not actually bad for that person's soul.
