Can I use GSEA to look for enrichment in data that is grouped into sets but are not necessarily genes?
Yes, if you have a ranked list, you can use GSEA to calculate the enrichment of the strains along the ranked list. 

Note that hypergeometric test is for count data, so you would test if there are more strains of one type that fit on certain conditions. 

I would recommend this article comparing different enrichment methods to understand well what they do.