You should read this :

http://www.rodoslovlje.com/en/groups/researching-ethnic-serbian-ancestors-austria-hungary

To trace and research family in the old country you need to know the original spelling of the first names and surnames, the exact village that they came from ( Bileća is  listed as parish or municipal centre) , the family patron saint (slava).

Also, information from US censuses and ship manifest is pretty much useless for going back in time - please find out which church your ancestors attended in the US and obtain scans of original church vital records .Besides more accurate spelling of their names and surnames, original household number in the old country is often listed, and that information is crucial if you are going to ask municipal office or an archive to do a lookup, or contact descendants of the same family.

The article with researching strategies tells you how to contact the Serbian Orthodox Church - in your case it is important because they will possibly have  records of donations GAJO TRKLJA made, and the names of the family members he purchased the headstones for would have been metioned as a part of the religious ceremony of blessing of  these headstones  when they were erected. The church record of such mentions is called "pomenik" and you will need to ask if it is available for the period and for the parish you are researching.

I do not do guessing and I cannot tell you the original spellings of the other surnames you mentioned without more information  ( place of origin for "Churich or Duicich" - there is about a dozen surnames from Bileća for that period that  could be the original one , "Milehjavich"  - where the info on Montenegro is from). 

Valid first names would be PETAR and ANA, Petar was a "hajduk" .

 I will look up TRKLJA family from Bileća area in historical records   and public databases for you . All TRKLJA families have roots there, in the villages Čepelica, Mirlovići, Podosoje  and Korita ,  and are blood relatives. The patron saint day is celbrated on 21st of November, Aranđelovdan

Bileća town was & is located in Bosnia. Your ancestors were ethnic Serbs and subsequently they would have indicated their country of origin as Serbia or Yugoslavia in the US censuses- that causes a lot of confusion among people researching them .

From personal knowledge - the Trklja family of my primary school teacher  is originally from the same area, they migrated to Vojvodina after the WWI ended (1918) when the volunteer fighters were awarded land  to settle there. They have a  GAJO TRKLJA  in their family tree and are probably related to your ancestor - according to the naming patterns and traditions and the date of birth, their ancestor would be the son of your Gajo Trklja's paternal uncle ("stričević").

Pomaze Bog! I know you are not a priest and it is missing some of the characters due to translation. Thank you for your response. Unfortunately, we have so little info. I believe the origin was Hercegovina. Surname was Trklja, do not know for sure the exact spelling of the first name and do not know the Patron Saint. The original church in the US they attended is no longer and the records have vanished. I checked with the Church that is only a few miles away and Father Radioich has no records. I do have one thing that I will pull out and look at again and differently. I found the article very interesting and many good things to know. In regards to the Churich or Duricich . . . this was his first wife and that is all I know. The Churich came off the son's death certificate. Milehjovich was his second wife and we also know nothing else about her.  The history is very confusing and a continuing education. I did not know about the Bosnia. I am very interested in your teacher's family. Again, thank very much for time and attention to our inquiry it is greatly appreciated. Mizpah

clarification ( i sometimes forget to explain in detail things that are backgound knowledge to us local people)

- Bileća is in Hercegovina . Hercegovina is a region, a part of the country called "Bosnia and Herzegovina".    People of all three etnicities who emigrated to US identified it as their *country of origin*.

If you ever plan to make a trip down there, my good friend and a great Serbian chef who lives here in Budapest, Hungary has family and can help you organize the trip.  Here is a blog in English about the adventure on which he took some friends for a visit to the area:

http://biztos.com/bileca/

The old photo of the valley before the lake will show you where one of the villages TRKLJA family is from was located.

Good Morning, I hope this finds you well. I was touching base to see if you have had any luck with research on the Trklja's & in regards to your primary school teacher?
Hope to hear from you soon.
Thank you
Mizpah
Dee

I wanted to also thank you for the link. I do hope to one day make a trip over and when the time comes I will contact them.
Thank you
Dee

Due to the fact that SGS Rodoslovlje consists of only volunteers, and the fact that it takes a lot of time for contacting people via emails and telephone to be able to track a single family, we are  only able to do that on behalf of our registered members. I have personally made some exceptions  to  this - like in the case of families devastated by the WWII:

https://www.facebook.com/rodoslovlje?filter=2

  but I simply have no resorces or time to continue doing so .  Check out the Austria-Hungary research group, we will post there an article soon explaining how long and difficult the process of reconnecting a single family is and what it takes to do it.

http://www.rodoslovlje.com/en/documentation/austria-hungary

We provided you general research advice and indicated where to look - but without looking at original documents or new information like household number and original spelling of the surnames of connected families it would take months.

What I can do for you is post any additional info here if I come across it , and post for you the headstones of the Trklja family branch in Vojvodina - I will have the photographs from that cemetery in two months time.