Yes, they all mean the same thing. However, I've never heard anyone use "I will mary." I think the most natural way to say it is "I'm going to get married." "I'm getting married (on the 14th of June)" is also natural.

These are all correctly composed English sentences. Each could stand on its own or be part of a larger sentence. However they do not have the same meaning as the sentences refer to different things These three refer to future actions. I will marry. I will get married. I am going to marry. The sentence immediately below could be either a future action or something happening now. I am getting married. as in I am getting married ( tomorrow). (future) I am getting married (at this moment). You would have to have more context to decide if it was future or present. Also note that your voice is important in understanding what is being conveyed. I am using (brackets) to illustrate the possible unspoken part of a sentence. For example using "I will marry" could be used to convey resignation. as in "I will marry (but I don't really want to )" could be conveyed by a flat tone with no sounds being louder and tending to fall away quietly. or determination as in "I will marry (and there is nothing that you can do to stop me)" could be conveyed by raising "will" loudly in mid sentence.

"I will marry" usually includes who you intend to marry. The rest are different future forms. Note that Tim's example of "I'm getting married" includes a date - with this form, we mean there is an arrangement in place.