You could probably use all of them.
I'm cooking now
Suggests the cooking has already started, or perhaps will start immediately as you put the phone down.
I have to cook now.
This is my choice because "have to" means that you don't have a choice. It is polite suggest that you would like to talk for longer but you must start cooking dinner.
I'm going to cook now.
This is fine, it suggests that you will start cooking right away. The future action (cooking) is a result of your present situation (it implies you are hungry)
I will cook now.
Rather to formal and plain, but correct.
I'd use the "have to" form, for the implication that "I want to talk more but I don't have a choice".
We would probably use an object "have to cook lunch", and there would probably be more conversational fluff.
Okay, look, I have to cook lunch for myself now, so um I'll talk to you again tomorrow. Bye for now. Take care, Bye....
or something like that. Actual spoken English is rarely that clear.