Does the صيغة الطلاق (divorce pronouncement) take effect by the husband's words to his wife: "Go to your family and enjoy yourself today; I am divorcing you and going to my friends," if he intends it as a joke and does not intend divorce?

A clear divorce, whether said seriously or in jest, is effective. The husband's statement "I divorce you" causes the divorce to occur, even if he is joking, because it is a clear statement that does not require an intention. The Prophet, peace and blessings be upon him, said: "There are three matters whose seriousness is serious and whose jesting is serious: marriage, divorce, and رجعة (taking back a divorced wife)." He can take you back during the waiting period (iddah) without a new contract, unless this is the third divorce.