<p>I'm wondering if a Java library can be called from a VB.net application.</p>

<p>(A Google search turns up lots of shady answers, but nothing definitive)</p>

No, you can't. Unless you are willing to use some "J#" libraries (which is not nearly the same as Java) or
IKVM
which is a Java implementation that runs on top of .NET, but as their documentation says:
IKVM.OpenJDK.ClassLibrary.dll: compiled version of the Java class libraries derived from the OpenJDK class library with some parts filled in with code from GNU Classpath and IcedTea, plus some additional IKVM.NET specific code.
So it's not the real deal.