Is it easy for any lay listener to identify a Richard Rodgers composition as his own, even given the three distinct styles? His stint with Hart tended towards the light-hearted and frolicsome, with songs that more often than not served as fodder for the Great American Songbook. There was a distinct classicism that leant towards operetta during his years with Hammerstein and in his post-Hammerstein career. I can't help thinking that these styles may be different, but yet by the same man.

Rodgers..in spite of being a despicably grouchy and rude man was a brillaint composer.

His years with Larry Hart showed his Jazzy,almost Cole Porterish style. with Oakie from 42-60 he hsowed a ore classical sweeping style.

ech of his hsows after O.H. death showed a respect for the material and style. "Rex" for instance is what i feel to be one of his 3 great scores. he evoked te mood and aura of Tudor England as easily as he would have evoked the clubs and bars of Pal Joey or the open plains of Oklahoma.

That's a very logical argument. And we have some source material to confirm that Rodgers only sought to "imagine" the atmosphere of his musicals when he was writing the music. A good thin about his "imagineering" is that he had a rough idea of the colours he music was expected to have. He was successful in capturing the exoticism in South Pacific and the Orientalism in The King and I. And let's not forget a certain fairytale quality to Cinderella that probably suggests some of the Disney animated films, and especially the Austrian quality of The Sound of Music.
But let's take the discussion further to find out what makes his music identifiable regardless of the time period of each of his songs.
I've thought that in the fountain of melody that was Rodgers, the thread that he used to tailor his songs seemed to be his endless melodies that move effortlessly from high notes at the upper end of one octave to lower notes at the end of another octave. I can see this in the first line of the refrain of Manhatten and in the first phrase of Blue Moon. But I think this is perhaps more pronounced in many of the songs he wrote with Hammerstein. In Oh, What a Beautiful Mornin', the first phrase of the chorus goes down and then up to a flattened seventh on the word "mornin'" to soar you to untold heights of elation and happiness. If I Loved You opens with a phrase that goes up on the first line and then effortlessly down on the second line "time and again I would try to say." Some Enchanted Evening repeats the same sequence of notes three times except that the second and third times reach to higher notes, before the melody goes down to lower pitches until it reaches up with the line "that somewhere you'll see her." And let's mention The Sound of Music and Edelweiss, because the ebb and flow of these songs from lower notes to higher notes is so effortless and natural.
I really think that perhaps the way his songs ebb and flow from lower notes to higher notes make his style easily identifiable, regardless of which time period his songs come from.

you stil only mentioned mostly his work with Hammerstein and 2 instnces with hart. lets not forget he wrote more songs with Hart than Hammerstien and 4 shows with others after Hammerstien's death.

Pinpointing the specifics of a style is very difficult, particularly for a 'lay listener'. Both you and Dawn have pointed out that, in general, there is/are (at least two) distinct phases in his body of work. This is not only influenced by his collaborators but also by the journey that musical theatre traveled during Rodgers' lifetime - for which, of course, he was partly responsible.

Furthermore, Dawn has raised the point that each of his works post-Hart have distinct stylistic languages that are related to the content of each musical. So to get back to the original question of the thread, I don't think it would be easy for a lay listener to stylistically link two totally contrasting Rodgers pieces, say "To Keep My Love Alive" and "Climb Ev'ry Mountain".

However, using the logic that Yip proposed in his/her latter post, yes, I think it may be possible for a lay listener to recognise certain patterns like upward phrase patterns - like those that exist in "Some Enchanted Evening" and "Getting to Know You". But even that is, I think a little too complicated. You'd have to have a structural knowledge of music, and be aware of how tempo, rhythm and lyrical phrasing can create variations of a structure.

So perhaps a lay listener would be able to recognize a pattern that is point it out. He/she may subsequently be able to identify a pattern and even articulate it, but by then he/she wouldn't be a lay listener anymore.