Firstly: "o'clock" should not be used except after a number of hours, alone. "12 o'clock", yes; "12:01 o'clock", no; "noon o'clock", no. If you need to be clear that (for example) "ten fourteen" is a time, and not some other number, you could use "a.m."/"p.m." or say "fourteen [minutes] past ten".
Secondly: "on the dot", "sharp", and others are used to emphasise that a time is precise when people might think it's not. If I say "12 o'clock", you might well assume that I'm rounding to the nearest hour (or half-hour, or 15 minutes, or whatever). I could say "12 o'clock sharp" to be clear that I mean exactly 12 o'clock.
If I say "10:23", however, the fact that I bothered to specify a number of minutes, and not a nice round multiple of typical values, would suggest that I mean exactly 10:23. Saying "sharp"/"on the dot" would be redundant in this case, but not wrong.
That said, there are situations when even an atypical number of minutes might be taken as vague, and so "sharp"/"on the dot" would not be redundant:
When accuracy to within seconds is meant, and you want to be clear that you mean "10:23 and zero seconds". (Example: A school has morning break start at 10:23. The students want to be let out 30 seconds or a minute early, but the teacher is adamant that they will be let out at "10:23 on the dot".)
When atypical numbers of minutes are still only estimates. (Example: Bus timetables will give times like "10:23", but it's expected that it will likely be later. You might then tell a friend that the bus arrived at "10:23 on the dot", because you want to emphasise how unusual it was that it was there right on time!)
Lastly: "high" is (in my experience) only used with "noon"; not just the time "noon", but with the exact word "noon". The title of the movie you linked to, "Twelve O'Clock High", is not about time, it's about direction. In a military (or colloquial) context, directions relative to you can be specified by points on the clock: "12 o'clock" is straight ahead, "6 o'clock" is behind you, "5 o'clock" is behind you but a little bit to the right. And then aviators, having to deal with three dimensions, can also specify "high" or "low" (or, if I remember rightly, "level"). So the title "Twelve O'Clock High" is pilot-speak for "straight ahead and at a higher altitude".