I checked my database and exported all STOIK persons from Posen area for you (see attached pdf-file attached to a separate email to you). It is very important to know the given name of your g-g-grandfather STOIK to get some success. At least the year of his emmigration to the US might be helpful.
I intend to check the big offline emmigrant database, which is located in the Museum in Bremerhaven, Germany (contents over 7,5 Million names)next weekend. I will try to find some STOIK persons, if I have some more information.
Additional to the attached information I found a Theodore Martin Stoik, married to Elizabeth Ann Czamanske at www.ancestry.com. Does he sound familar to you?