How do I know how strong my Irish roots are?

Sound like your sister is what they call “black Irish.”

Any Irish from your mom? If not you know you’re below 50%. And what do you know of your grandparents? And where did they come from? If you can go back just a couple generations you’ll get a ballpark estimate of how Irish you are.

I think how strong your roots are is a different question from how ethnically Irish you are. You can research your family lines on both sides, and that will tell you one thing. But how strongly you feel your ties to that part of your heritage is as much a matter of feeling and attitude as anything. I’ve known people who had just one Irish or Scottish grandparent, and that’s all, who really felt a strong bond to that part of their personal history. You can make as much or as little of it as you want to.

You should do a genealogy on your family.

DNA testing will verify strength of Irish descent.
I have heard of grandchildren taking after a Great Great grandparents genes.
So it is not unusual.
http://ghr.nlm.nih.gov/
website to learn about how genetics play a part in families.

Sorry I just noticed it says “just my sister didn’t cheat” I meant “trust me my sister didn’t cheat”.