Welcome to the forum.
Good but controversial questions, to some anyway.
You can read more about lineage on the eikoku roshukai website here: http://eikoku-roshukai.com/index.php?title=MJER_History
The above lineage explains in some detail the different branches. Soke Oe Masamichi did not name a successor and from his senior students three branches emerged (Hokiyama, Yamauchi and Masaoka). The current leader of each of these branches now seem to be affiliated with one or another japanese budo / iaido association and call themselves Soke.
To be frank we (as a group) don't have a soke, and we never had one. Iwata Sensei was our acting soke. He himself trained in Kochi for a period of years with senior students of Oe Masamichi (17th Soke), one of Iwata Sensei's teachers later became 19th Soke (Fukui Harumasa). Iwata Sensei received Menkyo Kaiden from two of these teachers. Menkyo literally means license and in MJER that has been seen as a license to teach the ryu to others.
The teachers who are carrying on Iwata Sensei's teachings are Yabe Sensei and Nishimoto Sensei. If you have been to either of the past two summer seminars you will know them as our teachers.
Meanwhile probably the only man, in my humble and probably much contended opinion, that you could call MJER Soke is Muranaga Soke who resides in Kochi who was named by Takeshima Soke to be his successor. This is explained on the shoshinshaz.com link in the message above yours.
I'm expecting much heat from this discussion if anyone else should join in, so I hope it answers your questions.