TL;DR: 1-2-3 Magic: Effective Discipline for Children 2–12 by Thomas W. Phelan
Ah, the joys of parenting. You haven't said anything about if he has siblings, and if so, where is he in birth order, and how he treats them.
Please allow me to go on a bit about ODD since it sounds like a possibility. ODD kids often: are very bright, get angry, argue with adults, refuse to obey requests/rules, deliberately annoy others, accuse others of their own mistakes or bad behavior (trust me on this one: they lie and are good at it), are susceptible to/easily annoyed by others, are resentful, are often rancorous/revengeful, don't think that they act in an oppositional way, but rather they believe it is a problem of others and that others make unreasonable demands of them.
Frequently, the parents say these children appear to be: insensitive to punishment, unimpressionable, difficult to deal with, risks takers, daring, very insensitive to punishments and physical harm. They appear to be exceptionally tough as though pain does not affect them. The possession of these character traits from the early years of their lives is significant because of the experiences which they produce and the reactions which they provoke in others. It is very likely that these children cause more conflicts and problems than the majority of children but, because they are so recalcitrant to punishment, they also receive more than would be needed to control the majority of children of the same age.
Oppositional Defiant Disorder usually makes its appearance before the age of 8... The negative symptoms usually flourish in the family environment but, with the passage of time, they may occur in other situations. Their beginning is typically gradual and usually lasts for months or years. ...[M]any children who suffer from this affliction never have serious problems as [adults]. Oppositional children openly show their unease and tension and use them both to annoy others and also to seek attention and care.
Basically, kids with ODD drive their parents crazy, and it gets worse as they get older. But the disorder is named primarily for the opposition, and that they do very well. If you think he might have ODD, it's really good to know before they continue for years in this path. Though many kids with ODD become fine, stable adults, some do not.
Also, there is a biological component (not always obvious.) Did you or your wife have a sibling or a cousin that drove their parents crazy, was always late for school, got kicked out of high school or was always getting detention, etc., or landed in jail?
That's enough scary stuff. I'll try to answer your question now.
There is a short but miraculous book called 1-2-3 Magic: Effective Discipline for Children 2–12 by Thomas W. Phelan (the book I used was the earliest edition) which outlines a way of giving time outs without argument. You said he doesn't respond to time-outs, but... if you and your wife do this each and every time he disobeys/acts out/needs discipline, it will eventually work, and it will help him as well, to learn to build up his tolerance to frustration/not getting his way. But one of the reasons I recommend this especially for the oppositional child is that once the method is explained and discussed with your son, you don't ever have to argue with him, raise your voice, or lose your cool again, you simply have to say, calmly, "Goeffrey, that's a one", to which he will howl and ask you what he's doing wrong (trying to get out of it; if he really doesn't know, you might need to explain, but nothing more), etc., whereupon you say, "Goeffrey, that's a two", and if he continues, you say, "That's a three. Time out." and he goes to his time out spot, whether you have to carry him or not. The wonder of it is that you do not engage with him in (what will often become an) argument at all. There are lots of suggestions for time outs, positive reinforcement and things like sticker charts for the times he does respond by controlling himself. (I used to keep small toys my kids loved in the house to give out immediately once a pre-determined and explained number of stickers was reached.)
Also, when he gives you an order, once you've explained that people don't ask like that (and he is expected to accept your answer and discuss it calmly if at all), all you have to say is, "Geoffrey, that's a one". If it sounds blissful, that's because it is.
ADHD is often a co-mormid condition with ODD. It used to be that kids were not diagnosed with ADHD before the age of six, but that's no longer true. If in doubt, get him tested by a reputable child psychiatrist (my personal preference) or, a child psychologist who specializes in ODD and ADHD. It's been my experience that the psychiatrists are much more proactive (and not necessarily with drugs.)
I'm truly sorry this is so long and so negative. I really empathize with parents who have oppositional children. I know there are things that help. I know life can be much more joyful in the home. And, once he starts behaving (and he will), you will be able to talk more, and enjoy more, give more, respect more, listen more, and struggle less. You will have asserted your authority without anger or being physical, and he will learn that there are consequences every time he misbehaves. You will have modeled calm parenting, which will become his default position as a parent himself.
GIFTEDNESS AND ASSOCIATED DISORDERS: OPPOSITIONAL DEFIANT DISORDER
**How can I teach my son that we as parents have authority over him;** that this is not to open to discussion; and that it is not a two-way street?I have great respect for you, but absolutely none for this statement. "Final authority", yes, for now, but "not open for discussion"? I could see "not open for argument", but discussion is a way we teach and ought not our children learn how to reach rational decisions in a reasonable manner? Maybe just choice of words in your post, but whenever I face the indomitable, I fight.