I would use WordNet as a database of relations for such words. But I have no experience with available Java interfaces?

Yes, you can use several well-known WordNet metrics via a Java interface such as this one:

WS4J (WordNet Similarity for Java)

http://code.google.com/p/ws4j/

Alternatively, you can use a distributional semantic similarity algorithm which, instead of a knowledge base (such as the WordNet), relies on a corpus of text in a given language. There are several Java libraries which implement distributional models. I had experience with and can recommend the S-Space Package - it contains a number of different algorithms:

http://github.com/fozziethebeat/S-Space

You could also try out a neural language model such as the popular word2vec which has been ported to Java:

http://deeplearning4j.org/word2vec.html

I can recommend the DKPro Similarity framework: https://code.google.com/p/dkpro-similarity-asl/

It implements many similarity measures already, including lexical similarity based on WordNet and other resources.

https://dandelion.eu/