Want to get in touch with my heritage. (Oklahoma?)

I was born here in the US (Oklahoma City) . My mothers family came over from Warsaw a few years after my mom was born. My grandfathers mother wanted them to become Americans so they basically but their Polish/Austrian heritage behind them. which I find to be very strange and no one will talk much about it. My grandfather is the only who has given any information as to why they pretended not to be Polish. The only thing he has ever said is that the relatives that were left behind in Warsaw have negative feeling towards us. Weird. So I am Half Polish and Half Austrian and I want to get in touch with my heritage. I will be getting married in March and have plans to start having a child soon after and want my children to know their heritage also. Any advice or have any ideas?????

You can do your own genealogy research online at a number of different ancestry websites.
Some of these sites cost money, like a membership fee, but if you look hard enough you can find most info for free.
I have a similar situation on my mom's side of the family: They are all of Austrian and German ancestry, but don't ever talk about it.

So, I went to the local library and actually pulled census data and other government records.
If you have the time, this is the best way to go.
Then you will have some answers about your roots and you can pass this on to your children one day.
(by the way, my grandparents on my dad's side were born in Cleveland county, OK and live in Norman, OK) :-)

Check: Naturalization Records, Ships Records, Military Records. All of these will give you clues.
Check: The history of Poland, Maps. This might tell you why they moved.

Check names at: JewishGen

For us to help you, we need names and dates.