The Ellis Island website is listing 3 KODRIKs passing thru that port to America. There is Marton/Martin Kodrik passing thru in 1906, he does have that he is Slovak and there is Finrich (Imrich on the manifest)too. Imrich is going to Pittsburgh, PA br-in-law Johann Slomka. Marton is going to his brother Kodrik Youre (could be Juraj/George).
The Slovak phone site at
www.zoznamst.sk is listing the name Kodrik.
You will need to locate a name of a town for you ancestor in order so you can research. The LDS-Mormons have filmed church records so when you do have that town name, check out their website for films which you can order for a small fee
and gather ancestral information.