Do you have any suggestions for how to research my Jewish ancestry?

I think I’ve mentioned this on Fluther before, but I did 23andme awhile back and was surprised to find out I had about 30% Ashkenazi Jewish blood. My dad then did both 23andme and AncestryDNA’s tests and got 45%-50% Ashkenazi Jewish. Now our minds are totally blown because this pretty much means my dad had 2 full Jewish grandparents – possibly a full Jewish parent – without him ever hearing a thing about it.

I’ve begun researching my ancestry and have figured out the tree going a few generations back. But how can I find out if any of these people were Jewish? I haven’t seen any stereotypically Jewish names in my lineage or any records of folks being buried in Jewish cemeteries.

I have very few living relatives to interview. My dad’s mom is alive but quite senile. And she’s the only person from my dad’s side of the family I ever got a chance to meet. It was a small family where sadly many people died young, before I was born.

Any help appreciated, thanks.