I am not a native speaker but -nakereba naranai/narimasen, -nakute wa ikenai/ikemasen and -nakya are the three ways that I learned to say "to have to do something". For instance, 1. Ima watashi wa ikanakereba naranai. I have to go now. 2. Watashi wa sono hon wo yomanakute wa ikenai. I have to read that book. 3. Watashi wa kare no kuruma wo arawanakya. I have to wash his car. "Iki" is the literary form of "itte" which means "...and I go". For instance, "yuube watashi wa mo-ru ni itte, eiga wo mita." = "Yuube watashi wa mo-ru ni iki, eiga wo mita." = "Last night, I went to the mall and I watched a movie." Therefore, "Ike" is the literary form of "ikete" which comes from "ikeru" meaning "I can go." -eru/-rareru is an ending meaning "to be able to." So ikeru = iku koto ga dekiru.

行かないといけない consists of 行かない + いけない, which is double-negative. If you've spent a lot of time with Japanese people, you've probably realized already that many of us use double-negative in English a lot because w-negative is pretty common in our language. As for 私は行け, we understand what you mean but unfortunately the saying is grammatically incorrect. It sounds like an order to yourself like Go Myself Now.

Also, I think "naranai" in this case is the word meaning "not good / bad / wrong" instead of "don't become" (negative of naru). Hence the literal meaning of "Ima watashi wa ikanakereba naranai."' is "If I don't go now, it would be bad / wrong / not good." which is the same as saying you have to do something, I think. So I believe that is why a negative from of iku is used here. Perhaps a native can confirm this or give a better explanation.

Some ways of the negative form of "to go" are: I don't go = いかない、行きません I can't go = 行けない、行けません、行くことができない、行くことができません Don't go (imperative but sounds like an order) = 行くな (sometimes it's translated as 行かないで on the subtitles depends on the tone of the voice.) Please don't go = 行かないで、行かないでください We use 行かなければならない / 行かなければいけない / 行かなくてはならない / 行かなくてはいけない / etc for "have to go / must go". I think it sounds like negative forn in Japanese but it doesn't. (*行かなければなる / 行かなければいける (/ etc) don't exist.) So, the oposit phrases are: I don't have to go / I don't need to go = 行かなくてもよい / 行く必要がない I mustn't go = 行ってはいけない Don't go = 行くな Please remember that these translations are very basic ones and there are many cases that they are changed, especially on the subtitles. I hope I could explain well and this was helpful.