If I cut an onion in one direction (into slices) with a meat knife, and then cut it the other direction (chopped) with a dairy knife. Both knives had not been used in 24 hours, but had been used for hot dishes in the past.
The onion should not be used, this is because the onion itself has the absorbed taste of both the meat and the dairy, and therefore it shouldn’t be used. Regarding the knife, based on a number of factors it would not need kashering, (However there would be a benefit to actually kasher it, and it is very easy. Just clean off the blade and stick the blade into a pot of boiling water). To say that the knife became trief we need that both knives were used for kli rishon meat and dairy, which is not so common. Aside from this there are opinions that with an aino ben yomo it is permitted.
Pri Megadim O:CH 447-13, D:T Y:D 96- 3,5, Chjavaas Daas 96-6b, Pischei Halacha pg. 327, Horav Y. Cahen shlit”a