Theres only one way to use nukes.
After around 40 turns, you fire 2 icbms at every single city you see. This will kill 99% of their units... and then you can finish the job with axemen and warriors.
I'm far from an expert(infact I've only made it to noble)so correct me if I'm wrong. Do you actually have icbms and still using warrs & axes? Maybe I'm more militarily minded but by the time I have icbms my warrs and axes would have been upgraded long ago.I'd have Tanks,infantry,planes,ect by then.Nukes or not.If you attacked me with warrs and axes you'd lose.