From the information that you provided it appears to me that his father has the same name. And if the surname of the father begins with an H then the same letter is showing in the mother's name. So I think the name is Halus. Google search gives Halus as a Polish Czech surname. I see somethingin the line below that looks like the name Maria. But I am not familiar with this language or how how the information is actually placed on this page to know where this information fits

I can get you a little further, but I would recommend you consult a Hungarian speaker. All of my Hungarian knowledge was acquired from this FamilySearch resource link below and using Google.

https://www.familysearch.org/en/wiki/Hungarian_Genealogical_Word_List

The header of this record is in Latin. But the record contains local Slavic names with Hungarian stock recordkeeping expressions and Hungarian notes. The handwriting is in Cyrillic at times, and this may also be true of some of the Hungarian words (so there may be Hungarian, written in Cyrillic, in this book). That means that the cursive will have letters that look readable to English-speakers, but they do not represent the same sounds. I also wonder if there are any handwriting idiosyncrasies or local versions of the cursive that might do unexpected things. For example, in English cursive, I always formed my capital Q's to look like a Q rather than the "2" resembling shape that was the correct version that I was taught.

Here's what I get out of the record:

1885 May 19

Mihaly (implied son of) Holyinka Mihaly, Haluska Maria (then likely two Hungarian words, one of which is kis) (kis means small). I think the mother's name is Haluska and runs onto two lines, just like Anna's name in Anna Belavics below.

Paulina (implied daughter of) Komjath Peter, Anna Belavics (likely Hungarian words -velok leany) 

Leany means daughter, so the Hungarian words are there to designate relationships.

Just a guess - one of the words that is repeated on the Groom line seems to be "admivelok" and perhaps this just means "legitimate son" or is just a formulaic, formal way of saying "child of".

Domicile:  (groom) Ydliri? (where the Y would be a U sound) Szerednye; (bride) Szerednye

More guessing…the bride and groom don't have street addresses, so they were likely living on farms or in villages that didn't have numbered houses. So the groom may be from the outskirts or some geographic designation that's slightly different from the bride's village.

Religion: Same religion, and I'm guessing "Greek Orthodox Catholic". I would expect that "g" to look different in Cyrillic. In entry 14, the groom appears to be Roman Catholic based on Cyrillic letters, while the bride is different. If Greek Orthodox Catholic, you should learn about Carpatho-Rusyn heritage and determine if that applies to your family.  You may already know this from the churches they worshipped in, in the United States. Greek Orthodox and Byzantine Rite for people who are not ethnically Greek from Greece would likely tie into Carpatho Rusyn heritage.

Ages:

There was apparently some uncertainty about the groom’s age (probably they didn't know his birth month and date to calculate it exactly).  They wrote two likely Hungarian words above the entry.  One is “eve” which means year.  Then 1861 and 23 eve (year).  Looks like the extra information is just to deduce the groom’s age, which is approximate.

The bride was 18.

Next columns are about single or widowed status.

Bride and groom are clearly single.  I’m not sure why the words differ across entries.

I read “legeny” (young man per FamilySearch term list) and something like “layadov” for the two entries.

The next set of names are the wedding witnesses and their religions (all same as the wedding couple). These are in the ballpark but might not be 100%.

Prokopecz Baril or possibly Bazil, Greek Orthodox Catholic

Gubanics Maria, Greek Orthodox Catholic

Szercso Andras, Greek Orthodox Catholic

P- or D- aurecicz Julia, Greek Orthodox Catholic

After the witnesses are two columns with hardly any information.

The first is for the name of the officiant.  I believe the scribble means “same person as previous entry” and the officiant is at the top of the page. The name appears on different pages in what looks like a different hand.  Looking across three pages, it seems to be something like “Dlubaz, Sandor”. I'm guessing other people were recorders for this book since I'd expect his handwriting to be similar over pages. The forms of his name also look a bit different. So maybe the recorders had different language backgrounds.

The second column relates to banns and dispensations (for cousin marriages, etc.). So whatever the entry means, it seems to be typical (no special issues).

The final column is for notes/observations.  There is a long note which looks like it's in full Hungarian, but it might also be mixed Hungarian and local expressions.  I believe a Hungarian speaker would be able to translate this. Google Lens was not able to translate it.

The final column is an official note referring to the fact that the groom's date of birth was added later (you can see the different ink, it says "year of birth 1862, i.e. 25 years old"). It says that the birth was not registered by actual data, rather based on the witnesses testimony, which they made under oath. The last sentence just before the signature is a reference of some sort. The first two words are "E bizonylat", meaning "this note". I can't read the rest, sorry. :)

You are welcome, any time.