Anunia isn't quite right there.
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Eowyn and Eomer were brothers, and they were the sons of Theoden's brother, Eomund. Theoden raised them as his children. So, they are Theoden's nephews.
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Eowyn is of course a girl, and therefore Theoden's neice. Eomund was Theoden's brother-in-law: he was married to Theoden's sister Theodwyn, and Eomer and Eowyn were their children.