How I can understand that?
You ate something and now you are hungry. Or not? ;)

Similar to “I'm so hungry that I ate it”, but I think the register is supposed to be sort of rough to match the Japanese.

But hasn't it to be "I was so hungry, I ate it"?
The original sentence is, that I ate something and after this I am hungry.

@Espi
"I was so hungry, I ate it." (Likely, I'm not hungry anymore)
"I am so hungry, I ate it" ( Although I ate it, I'm still hungry.)

Yes, that I understand.
I want to translate it into German, but I'm not sure, what the correctly meaning is.

@Espi How about? "Ich habe es gegessen, so einen Hunger habe ich."

@Dejo: I'm not sure your German suggestion would match the register here as this one is intentionally terse. Perhaps something more like "Bin so hungrig, ich hab's gegessen" (I wouldn't feel comfortable saying for sure).

@Espi: If you're not sure what the precise meaning is, then perhaps best leave this for now. Adding a poor translation is just going to spread misunderstanding. Besides, there are plenty of other (more useful) English sentences waiting to be translated. :-)

@Dejo: Yes, of course. But better were "..., so einen Hunger HATTE ich."

@Swift: Thanks. You're right. I'll leave it for now.
I'll look for the next English sentences. Greetings ;)