How can I find birth and marriage certificates pre-WWI?

That's now Ciacova in Romania, and the records if they still exist will be there, not in modern-day Hungary. You need to be searching online for Romanian records, not Hungarian.

I don't know about Romania, but in some other ex-Hungarian lands like Croatia and N Serbia, the State Archives took over these records, since they were official records the churches were mandated to maintain.

Unless you speak Romanian, I assume you'll need some local help. Note that while old church records in modern-day Hungary have been well preserved, that's often not the case in the former lands. So don't be too optimistic at this stage.

You may have to hire the services of a person who speaks/reads Romanian.
The churches used to keep really good records but that was in Hungary as the other poster stated.
I hope you can work this out.
My husband's father had to prove to the new communist Gov. after WW11 that our last name was actually not bought or stolen. They called him into the police station a grilled him on why his name was spelled as it is. They demanded he change the spelling by losing a S or adding a ie instead of the Y.
He had lost everything and just wouldn't allow them to make him also lose his long time family surname.
He traveled all over collecting documents from churches and city halls all over Hungary. Was able to prove that our last name was not bought or just taken on, was allowed to keep the spelling.
Sounds like a minor thing but if they want to take away your name then what's next?
Just saying, the churches usually keep really, really good records.
My American cousin who speaks some Polish was able to go back nearly 300 years so far to our village in Poland and find my family roots, all through records kept in the churches. Even found a few Hungarians here and there.
Hire someone if you really can afford to do so.
I looked at the message board on Ancestry .com and found a message from one of my cousins looking for anyone related to my grandfather, this lead to a big family reunion in Poland a few years back and finding out allot more about our family. Maybe you can at least leave a message on their board and hope someone finds it sooner or later. My cousin had that message up for over 3 years before I noticed it. I was really blown away that we all met each other because of that one message, didn't cost a penny either.