I am Messianic, but I've never claimed to be a Messianic Jew; simply Messianic. I am not "under the Law," as only those who are unbelievers are "under the Law"; however, I am Torah observant. By saying I am Torah observant, I intend that I obey Torah as much as I possibly can, according to how I and my synagogue understand Torah. This means that I eat the only food as described as food and commanded in the Bible. I observe Sabbath and worship with my community on Sabbath. I have had my bat mitzvah. I do a miqvah as often as I can, but that is limited because of the area where I live.
I believe that I should observe the written Torah but observe the oral Torah in a limited way, as did Messiah. I believe that the Bible -- the WHOLE Bible -- has complete authority, but the oral torah is not authoritative. Torah, the first five books of the Bible, was completely about Messiah and His coming, and so is the rest of the Bible. I believe He is the coming King, the Prince of Peace, the Risen L-rd, the High Priest Who is ever interceding.
While I observe Torah, doing all I can in the absence of the Temple (and while not living in The Land), I am not saved by my works; I am saved only by the work of my Messiah. Nothing I do or don't do can improve my place in the world or improve it over those who do not specifically observe Torah. From what I understand, many Christians observe more Torah than they realize.