EU law does overrule Irish law in all those areas covered by our membership.
I'm not sure why you have suggested that there is no such thing as EU law. That's rather puzzling.
Directives are forms of EU law which are only binding to the members concerned, but where the mode of enforcement has not been specified, thus leaving it to the member state to choose the method by which it is incorporated, or as you have stated - 'transposed', into national law. Regulations are the most powerful form of EU law; they are immediately enforceable, binding in their entirety and applicable in all member states. Once they come into effect, they overrule all national law in the area concerned.
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