Hi Padma - As a partial answer to your question, Ohioans in 1920 would speak very much as people do today with the exception that some words which were coined after 1920 would not be in the vocabulary. My Dad was a 19 year old Ohioan in 1920. I have some things he and other members of my family wrote back then and there's no difference from modern speech.
There would (could) also be some differences depending on what type of characters you use. My Dad's father was the son of a German immigrant and used sentence constructions that were much closer to the German original. That type of difference would appear in any fairly recent immigrant families - but that's also true today.
There should be a lot of information available on the internet about schools. Try doing some Google searching using school Ohio 1920 and see what types of results you get.
There would be some differences depending on where the schools were - city or country. There were still some one room schoolhouses in use in Ohio in 1920, but there were also also larger schools. I live in a fairly rural area of Ohio and the schools in my community were multiple rooms. The elementary school had four rooms (two grades per room and a "play room") and the high school (which included 7th and 8th grade) had five rooms and a cafeteria. In both schools there was one bathroom for boys and one for girls; there was a sick room; and there was a principal's office. The high school had a gym attached with a stage for plays and concerts. There was a little dressing room beside the stage on both sides where "actors" could change for the next scene. The heating and cooling systems for the schools were in dark, dingy rooms in the basement. The elementary school also had a basement apartment where the school janitor and his family lived.
School subject matter was not quite like it is today. The students studied reading, math, English, and geography. At the upper school level science and languages were added. I have some of my Dad's grade cards from college (1920's) - his subjects were English, Latin, Greek, and Geometry - semester after semester.
I went to school after the 20's (obviously). My memory of elementary school is - 1st grade reading, phonics, and adding; second grade reading, phonics, adding, and subtracting. Third grade we added English grammar and multiplication to what we'd been studying. In fourth grade we added geography and division. There was tremendous emphasis on the basics. We still had two grades in a room, so everyone really had an opportunity to learn the two years worth of work twice.
Hope all of that helps you a bit. Puma