Many times I have seen vague references that if one has not cooked on a vessel for 24 hours at least, it can be used for kosher purposes. However other rabbis say that no matter what a vessel must be kashered to be used for kosher purposes. What is the halachic source for the matter?

After the fact, if someone has cooked kosher food in a vessel that had absorbed non-kosher food more than 24 hours prior to the cooking, the kosher food remains kosher. After 24 hours, the taste imparted from the food absorbed in the walls of the vessel to the food being cooked is considered spoiled and therefore cannot contaminate the kosher food (Shulchan Aruch, Yoreh Deah 103,5). It is forbidden, however, before the fact to cook in such a vessel before kashering it (see Shulchan Aruch Yoreh Deah 99 and 121).