I'm new to Esri's Arc* interfaces, and trying to figure out how to register an existing table using the ArcObjects API. The following question answers this to some extent:

Is there any way to write a snipet of code with function of "SDELayer -o register" command

Maybe the IClassSchemaEdit.RegisterAsObjectClass method will help (see the GeoDatabase OMD). You should be able to QI it from an ITable, opened in the usual fashion (e.g. IFeatureWorkspace.OpenTable(in Name: String) since you've already built your GDB).

But there is some terminology used that I don't understand. Specifically, what does it mean to QI something, and how is it done?

This other question's answer defines QI, somewhat vaguely, as Query Interface (hopping) but goes no further.

Navigating ArcObjects Object Model Diagrams (OMDs)?

It really helps if you know UML. In the class that I had in college the professor called it QI (Query Interface) hopping. The Getting To Know ArcObjects book has a nice break down of how to work with the diagrams.

I'm using Java - is this a .net thing?