Here is Naturalization info for Martin, you can obtain the paperwork at the National Archives at Chicago.Mary or Maria (Slovenian spelling) would have been made a Citizen at the same time
name: Martin Slak event: Naturalization event place: Joliet, Illinois event date: 1894 age: birth year: birthplace: Austria nara publication title: Soundex Index to Naturalization Petitions for U.S. District & Circuit Courts, Northern District of Illinois and Immigration and Naturalization Service District 9, 1840-1950 nara publication number: M1285 nara roll number: 158 film number: 1432158 digital folder number: 004641292 image number: 05545
Where did you find his ship manifest?I can not find it.
GREGORIC is a patronimic name, from the male given name Gregor (Gregory in Eng) IC ending means son of.
Have you checked the baptismal records for the children?Often times these will list the birthplace of the parents.
The online Slovenian Phone book has 202 listings for SLAK (sounds like slahk) and 470 for GREGORIÈ