Not being an orthodox mason myself, I can only take a stab at this question.
I am thinking the Lions Code of Ethics (with which I am very familiar) might go a ways to defining orthodox Masonry.
The Lion's Code of Ethics
TO SHOW my faith in the worthiness of my vocation by industrious application to the end that I may merit a reputation for quaity of service,
TO SEEK and to demand all fair renumeration or profit as my just due, but to accept no profit or success at the price of my own self- respect lost because of unfair advantage taken or because of questionable acts on my part.
TO REMEMBER that in building up my business it is not necessary to tear down another's; to be loyal to my clients or customers and true to myself,
WHENEVER a doubt arises as to the right or ethics of my position or action towards my fellow men, to resolve such doubt against myself.
TO HOLD friendship as an end and not a means. To hold that true friendship exists not on account of the service performed by one to another, but that true friendship demands nothing but accepts service in the spirit in which it is given.
ALWAYS bear in mind my obligations as a citizen to my nation, my state and my community, and to give them my unswerving loyalty in word, act and deed. To give them freely of my time, labor and means.
TO AID my fellow men by giving sympathy to those in distress, my aid to the weak, and my substance to the needy.
TO BE CAREFUL with my criticism and liberal with my praise, to build up and not destroy.
As the founder of Lions International was a Freemason, I rather suspect that their Lion might be one that we are familiar with.
Our birth is but a sleep and a forgetting…trailing clouds of glory do we come from God, who is our home -Wordsworth
I suggest the very term 'Orthodox Masonry' begs a number of important questions. For a start 'orthodox' is surely a term appropriate to a church, or some other institution possessing a dogma, to which one relates in an orthodox or heterodox fashion. But since Masonry searches for truth without any dogma, how can the term orthodox be applied to it at all?
A distinction also seems to be made between orthodox and esoteric Masonry. On what basis may one ask? At what point in its history did esoteric masonry cease to be orthodox--if one must use that term? Who has the authority to say that esoteric masonry is unorthodox, and on what grounds?
The great esoteric Freemasons of the past recognized that Masonry had esoteric and exoteric aspects, and when I read the works of McNulty, Leadbeater, Annie Besant, Wilmshurst and Hodson, to name but a few I don't recall any of them claiming that one sort of masonry was orthodox and another wasn't.
As a Co-Mason I naturally relate to the esoteric tradition, but it never occurred to me to think that Co-Masons are unorthodox because they express a different emphasis in their ritual workings, or that there is something wrong with those who interpret masonic symbols differently.
Also is there not a danger that if we introduce terms like 'orthodox' we can unintentionally slip into the mindset that categorizes people as orthodox or unorthodox depending on whether or not they agree with us. A bit like the argument about regular, or irregular masons; it's all too easy to think without realizing it that "you're irregular because I disagree with you."
They say Japan was made by a sword. They say the old gods dipped a coral blade into the ocean, and when they pulled it out four perfect drops fell back into the sea, and those drops became the islands of Japan. I say, Japan was made by a handful of brave men. Warriors, willing to give their lives for what seems to have become a forgotten word: honor. -The Last Samurai
I rather think that arogers has a point. Once we start making distinctions, we create distinctions. However, masons and even individual lodges do tend to take of some characteristics more than others.
Some lodges are devoted to fellowship, others to historical research, and dare I say some lodges adopt 'my way or the highway' attitudes towards their Freemasonry, etc etc
If a new person has a choice of lodges to join (within the one Order) it is very important to direct them to the one which suits their interest and temperament, don't you think?