I am from SLovakia. My grandmother is from Arvai family, from th neighbourhood of Nitra. I will go this year to the state archives to search for farther information.
But general information, that i can give you is, that name Arva means region of todays Orava-northern Sovakia. Suffix y, or i or j are comming from hungarian language, slovak equivalent is Oravec, also this name may be your family. It is because of complicated relationships and history of Upper Hungarian kingdom, todays Slovakia.
The surnames has been given during 18. and 19.century (After the reign of Maria Teresia) The byrokrats had to use hungarian language and in lots of districts they have overwritten slovak name Oravec to Arvay, then again it was change to Arvaj, or Arvai or Arvayi - all theese version are common in my family tree. It is quiet complicated. If you have any interest writte on xtruh@hotmail.com