The best place to find indexed post 1895 Hungarian (within current borders only, not what is currently Slovakia, so Zemplen may be problematical) is MACSE, the Hungarian Society for Family History Research. www.macse.hu
Their volunteers index the civil records available on FamilySearch. The results are only available through the MACSE database and not through the FamilySearch database. However, for each result there is a direct link to the FamilySearch image.
MACSE is fee for service. it's only$30/yr. The site is in Hungarian, but there is an English interface as well as a instructional video in English on how to use the site (available once you register).
As with all databases, it is incomplete, so you may find records for one town for one year, but not another, or one type of record but not another. The database is updated monthly, so it pays to check back periodically for new additions.
The Dvorczak gazetteer https://web.archive.org/web/20160410185836/http://www.radixhub.com/radixhub/gazetteers/1877/
will tell you what records (whether available on FamilySearch or not) are available for your town, but only covers up to 1895, not civil registration records. It is organized by megye. Just click on the megye you want, then use your computer's search feature to find the town you want. Find the column for Jewish records and you'll see whether a) there are records for your town, b) if they're enumerated with a different town and c) whether they have been microfilmed by FamilySearch ([FHL] means they have; otherwise, they haven't and you would have to contact the local archives to research them).
I have found MACSE to be indispensable for my Hungarian research. Good luck!
Fort Collins, Colorado, USA