You're right. All are the same meaning. You have to be careful to use them to whom. 「行きましょう」is the most polite phrase of them. You can use this to elder people. Or I would say "行きませんか？" This gives the suggestion to the person. I guess, it's same as "Shall we go---?" 「行くぞ」is a male phrase. If you use this to your girlfriend, she feels you're masculine. It's a bit strong word to offer someone to go with me. 「行こう」is a casual phrase and used to your close friends. I guess, it's same as "Let's go" to your friends. Sorry for my poor English. If you don't understand well, please let me know. Thank you.