We have an IBM UniData server. I just installed UniObject .net. It looks like you just issue unidata queries through the .net classes.
Where can I learn the query language/syntax and to work with UniData in general? What books, sites, or videos do you recommend?
The best resource is going to be Rocket Software's UniData library.
Rocket recently acquired the U2 family of products, which includes UniData and UniVerse, from IBM. They've got a pretty extensive catalog of documentation for UniData. You might want to check out the "Using UniQuery" document, which discusses the UniQuery in particular.
Unfortunately, you won't find many books, screencasts, or programming communities devoted to UniData because it's pretty esoteric. If you run into anything specific that you've got questions on, it can't hurt to post here using the UniData tag and I'll do my best.