I am asked to do the enrichment test and was provided a gene set with plenty of databases such as GO, KEGG, InterPro, IntAct, IntEnz etc.
How can I know which should be tested and which should not be? Is there any way to differentiate one from the other?
As already pointed out, genes are annotated with various types of information. Which one you use depends on the question you're trying to address. If you're asking something about cellular function then you want to use functional type of annotations. If your question is more about structure then you would want to use structure-related information. So you have two things to do:
1- Learn about the information that each resource contains
2- Figure out which resource relates to your biological question
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If there would be a clear answer what to use in every case for every organism, it would be easy! Also these things are also not quite equal, e.g. InterPro says "InterPro provides functional analysis of proteins by classifying them into families and predicting domains and important sites." while GO says "One of the main uses of the GO is to perform enrichment analysis on gene sets" or IntEnz "IntEnz (Integrated relational Enzyme database) is a freely available resource focused on enzyme nomenclature". So yeah, they do different things, even though these topics obviously are all kind of connected. I think you just should spend more time investigating each of these 'databases'. It's also probably time well spend. However, if you want to enrich genes there is no way of ignoring GO.