On the Ellis Island records, when it says Kielce, I think that means in
Kielce, and not near
Kielce. Back then, Kielce was the name of the state (Voivodeship) as well as the name of a city. So, Olesnica, Kielce is like saying Detroit, Michigan. At least that is my interpretation. Either way, I believe (without solid proof), that this is the town being referred to:
Olesnica is a rather small town, and Glowniak is not a very common name, so I would guess that we are related, but I do not know how as the information you gave above does not match the limited information that I have. Ludwik Glowniak was born in 1892 to Tomasz Glowniak and Francisca Ambroza. He came the US in 1909, and ended up in Detroit, Michigan.
In my research I have come across Stanislaw Glowniak, son of Joseph and Francisca Plewins, who married Eva Zowisza in Detroit. I don't know of a relationship to my family, and it does not sound like a match to your information either.
Assuming your grandfather was Roman Catholic, the church could hold records of interest (to both of us). Olesnica was part of the Stopnica deaconate in the diocese of Kielce. My belief is that any records would be in one of these cities. Stopnica was essentially destroyed during the war, so let's hope the records are in Kielce.
I think these types of records are held by the state archive. w w w.archiwa.gov.pl/en/news.html There is a state archive in the city of Kielce. I have not been able to verify that that is indeed where Olesnica records are held, or if any still exist. It looks like there is an effort to digitize these records. See genealodzy.pl/PNphpBB2-viewtopic-t-9884-postorder-asc.phtml There are also a few records that have been indexed at geneteka.genealodzy.pl They have an index for a Michal Glowniak born in Kotuszów in 1857. I don't speak or read Polish so I depend upon Google Chrome to translate, and it doesn't always make it easy to understand.
There may be some Russian records may exist as well, since at the time of your grandfather's birth, Poland was part of Russia.
I wish I had more precise leads for you as it would help me as well as I think we are looking for the same thing.
I think this is the web site for the parish in Olesnica: w w w.olesnica.republika.pl Somewhere is says that they only have records at the parish post WWII.
There is at least one Glowniak family still in the area, as young Dominik Glowniak came in second in the bible study contest.
It looks like my link to Google Maps was deleted. Here is the town I was referring to:
The LDS Church has civil transcript of Roman Catholic parish register of births, marriages and deaths of Oleśnica from 1875 to 1884 on microfilm. I have not rented these films. They do not appear to be online yet.
It may be that this this is all of the vital records (BMD) left after the war.