Translation:My oldest sister loves his youngest brother.
Hi, it actually does make sense :) - it does not have to be her own brother. For example, I may have a husband and say that my sister loves his (my husband's) youngest brother. It is the same in the Czech sentence - it also is "tricky" in this way, that the brother is not the sister's brother but HIS (some guy's) brother.
"My oldest sister loves HER youngest brother" woud be a little creepy in Czech (we mostly use "miluje = love" for romantic feelings) ... and would be translated as "Moje nejstarší sestra JEJÍHO nejmladšího bratra miluje"... as a matter of fact, that still does not sound so creepy because "jejího" could be another girl's brother. (For example we're talking about the brother of my female colleague).
If you said "Moje nejstarší sestra SVÉHO nejmladšího bratra miluje" that would mean it's HER OWN brother. Hope this helped :)... I agree it's a tricky one...