Summary

Yosef Karo Yoreh Deah — Orach Chaim 103

And if one cooked in it within 24 hours something to which the first prohibited substance gives a positive taste, then if there was not 60 times of the second dish more than the original prohibition, the second is forbidden. But if the first dish was stirred with a spoon and subsequently thrust in a second dish, which it also taints, the second cooking pot is not forbidden. And also in the case of something that has a totally neutral flavor, such as a honey pot where people melt honey, despite the fact that there are bee legs in it, the pot is not forbidden, and so too every similar situation.
Source: Wikisource

Yosef Karo Yoreh Deah — Orach Chaim 103

Anything which has a bad (pagum) taste does not render its mixture forbidden. And even if its taste is not bad on its own, for on its own this thing is tasty and great, but when introduced into a mixture has a bad flavor, this mixture is permitted. Gloss: But significant things like a birya [see YD 100] or the like, if they do not have a bad taste on their own, even though they make a cooked mixture taste bad, they are not nullified even if there is 1000 times the amount of it in the mixture.
Source: Wikisource

Yosef Karo Yoreh Deah — Orach Chaim 103

Oil and honey of non-Jews, despite the fact that they are boiled, are allowed. This is because meat makes the oil less flavorful and makes it smell bad; the same is true for honey. HGH: There are some who say that meat does not make honey itself less flavorful, but rather, a drink made from honey. And in a situation where there is not such a big loss, one should be stringent in ruling.
Source: Wikisource

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