I cannot say for certain as for the latter topic (Greek myth), and instead focus solely on the former one (Norse).
In short, reception of the Christianity among the Norsemen was probably not one-day, sudden change of the mind for many of them.
Recent scholarship on the topic instead tend to presuppose the relatively long (sometimes more than several generations of 'contact and infiltration' phase between Christianity and the Norse people, and some experts like Nordeide and Mikkelsen even claim now that this kind of contacts even predates the beginning of so-called the Viking Age.
Some Vikings in fact saw that the new religion (?) of Christianity and their old one were not totally exclusive each other. Though very hotly debated (possibly also in this subreddit right now), more and more researches agree that the medieval Norse myth stuffs in our hands now, especially represented by the famous work of Snorri Sturluson (d. 1241), were were no 'orthodox' in any possibility, and archaeological as well as very fragmentary contemporary written evidences suggests there were considerable room to keep their very local traditions or to adapt new traditions like 'there is a new supernatural, powerful being called Jesus, popular among the Europeans' or something that.
The Deed of Charlemagne by Notker the Stammerer, reports my favorite episode on this matter (II-19): Many Northmen took a visit in the court of Frankish Emperor Louis the Pious to get baptized, though some of them mistook the baptism as a kind of welcome ceremony and got baptized several times (I afraid it's too long to cite in detail, so search this linked dated English translation with '19. As I have mentioned the Northmen' to find the first sentence of the two paragraphs in question).
Some people (including the scribe himself) might laugh at their crude understanding of Christianity and its rituals, but more and more Northmen got acquainted with Christianity and its norms through the increasing contact with Europe in course of the Viking Ages, and it is likely that some of them gradually practiced some of Christian ways of life also in their original homeland (Scandinavia).
As the number of this kind of 'Christian' people increase in the local society, some social tensions between two norms of social life might have arrose, as best formulated by the famous word of Icelandic lawspeaker Þorgeirr in the Book of the Icelanders: 'Let us all have the same law and the same religion. It will prove that if we tear apart the law, we will also tear apart the peace (Chap. 7: The translation is taken from Grønlie 2006).
So, the 'day' you mentioned was probably the date that the majority of the local community in Scandinavia agreed that they would adapt and run their society solely based on Christian ways, and it was not the myths of the gods, but the social norms ('law' by Þorgeirr) that primarily mattered for the contemporary Norse people the most.
My possibly relevant previous posts:
Additional References: