I have an overseas taiwanese passport but no ID number in it.
I wonder what visa I need. I plan on staying in Taiwan for little more than 6 months. Is there a visa that allow me to stay there for more than 6 months without having to leave.
I also heard that they can stamp both your taiwanese passport and in my case my swedish passport when I leave the country. ( I will enter with my taiwanese passport). 
Donāt know about the āoverseasā Taiwanese passport. What color is it?
Yes, if you enter with your Taiwanese passport, when you leave, you can get your Swedish passport
My passport is green.
Do you also know what visa I need.
Your green passport doesnāt have a identity card number?
If you have the same passport that all ālocalā ROC nationals have, then thereās no problem for you to enter the country without a visa using it. As far as I know, there is only one passport, green. You just have to make sure when you leave the ROC, you get both the ROC and Swedish passport stamped when you leave. If you donāt, then the game is up.
Sorry canāt be of more help. You might want to check with the Swedish Taiwan Economic and Cultural office first with someone who can speak Mandarin fluently to help āsmoothā any issues.