I have have kept your structure, as it is easier on the eyes.
B: I am not hungry, either
B: Me, too [used a lot, colloquial, but OK]
B: So am I [preferred]
B: I am, too [preferred]
B: I am hungry, too [fine, but we do often contract this: I'm hungry too.]
A: I am not hungry
B: Me, either [colloquial, but it is used]
B: Neither/nor am I [preferred]
B: I'm not, either. [preferred]
B: I am not hungry, either [preferred], I'm not hungry either.
A: Mary is hungry
B: Tom, too [super colloquial]
B: Him, too, Her, too [super colloquial]
C: So is he; So is Tom; Tom is too. [preferred]
A: Mary is not hungry
B: Tom, either [super colloquial]
B: Him, either [super colloquial]
C: Neither/nor is Tom; Neither/nor is he. He isn't either. [preferred]
Super-colloquial is OK in some circumstances, but it does mark the speaker as somewhat uneducated. The super colloquial forms are often used by small children, too.
In general, when saying short things like I'm hungry, we use contracted forms unless there is a good reason not to, for example, for greater emphasis: But I am hungry.
Him, too and her, too can get rather awful in the plural: Them,too. So, I would advise being aware of them but not using them in your conversations.