I feel the need to say the state of one's sobriety is not an excuse to cheat. Cheating is cheating. You're in a monogamous relationship, presumably, and you get with someone else. Doesn't matter how drunk you are. It doesn't matter if you hook up with one person or thirty. There's no it was "better" because you were with less people than your girlfriend. It's still a poor choice, and one many people won't forgive.
I can't tell you whether to forgive your girlfriend or not. I will say that many of the choices you provide in your poll seem to be made out of an emotional mindset more than a reasonable one. That won't help you. Making choices based on feelings of hurt won't help you and, more than likely, will make things worse. You need to assess your own feelings and your own actions in how you took part in creating this situation. Then you need to assess your feelings about how you feel about your girlfriend's actions. I suggest choosing what's called the "middle path" in DBT: making choices using both your emotional and rational mind. Assess each option using the middle path. Do a pros and cons list of each choice. Try to pick what seems to have the most resolution with the least amount of fallout.
Only you know whether or not you can forgive her, but either way, if you do choose to stay, there's some major issues you guys need to work through regarding trust and communication. Keep in mind it may be impossible to get through this, but you can always try.
Good luck. Feel free to
PM me if you need anything else.