A small difference, I would say, but none that is noticeable and people can easily switch between the two in common speach. Since "blev" is past tense of the verb "blir" = "become" and "var" is equally past tense of the verb "är" = "be", the former speaks more about the logistics of setting up the party, while the latter speaks more about the feeling of the party.
Although they don't map precisely to one another, does "Kalaset blev mycket bra" correspond somewhat to "The party went very well", as opposed to "The party was very good"? The two have roughly equivalent in English, though the former might suggest more that it came together nicely, or went smoothly without significant problems.
Not 100% sure but I believe that 'ett kalas' is less formal than 'en fest'. Usually, 'en fest' is something that adults or teenagers would attend and 'ett kalas' is a party for children. However, this is not always the case as I have heard many swedes use them interchangeably but it is possible that they were saying 'ett kalas' with tongue in cheek.
All you said is true, though there is no real difference in formality between a "kalas" and a "fest". More in tone as you mentioned; "fest" feels more adult/hip than "kalas". For something more formal than those you could use "tillställning", or if it is big, "gala" (though I doubt a child would be appealed by either of those...)
The most common word for a crayfish party is kräftskiva.
I agree with tarekzein: kalas is often about children's parties, birthday parties, or parties where food is an important factor. Whereas fest focuses more on the partying aspect. Those are however just tendencies, there's no hard and fast rule.