Tokaido Shinkasen train

I will be traveling with my family of 5 this December. I am trying to but speed train tickets in advance from Kyoto to Odwara on 12/26 then from Odwara to Toyko on 12/27. Can this be done online from the U.S? Must they be purchased in advance? Does the train sell out? Thank you for your help!!

This can be done online in advance. System came online this month. Google "shinkansen booking online"

I think tickets become available 1 month prior to departure, if I remember correctly. So you have to wait just a few more days.

Enjoy your trip to Japan!

Here seem to be a few typos: you will change Tokaido Shinkansen trains at Odawara then head to Tokyo.

System came online this month. Google "shinkansen booking online"

That does not lead you to the new system(, at least currently).

At the end of October, new application software in English became available in the United States,
Australia, Singapore and Hong Kong for seat reservation in Tokaido and San(')yo Shinkansen trains.
This app is designed basically for passengers who pay regular fees by a credit card; you cannot use it when you travel with a rail pass which covers your Shinkansen train ride.
https://smart-ex.jp/en/beginner/

I will be traveling with my family of 5 this December.
from Kyoto to Odwara on 12/26 then from Odwara to Toyko on 12/27.

When you hope to go outside the Shinkansen gate of Odawara Station, you need Shinkansen super-express tickets separately for both the sections (until and beyond Odawara Station).

Is Kyoto Station at the end of your JR route?
A JR basic fare ticket which is good for 2 or more days allows you to make a stopover (outside the JR gates) at a station on the course which is specified on its surface.
You can get a JR basic fare ticket to travel from Kyoto via Odawara to Tokyo, which is good for 4 consecutive days.

Where is your first destination in Tokyo?
In Tokyo Metropolis there are two stations on Tokaido Shinkansen: Shinagawa Station and Tokyo Station.

Does the train sell out?

It will be probably before the peak of New Year travelers' rush, but your seats may not be in the same row or neighboring rows.

I recommend you try to reserve your seats.
Many school children will already be in a winter vacation, and there may be many passengers who choose to get packed in a non-reservation car than paying a few hundred yen more (per person) to reserve their seats.

In a Tokaido and San(')yo Shinkansen train, every Ordinary-Class car has seat rows each consisting of 5 seats: 3 on the on the one side and 2 on the other side.
http://railway.jr-central.co.jp/train/shinkansen/detail_01_01/seat_a.h...

For your information
: Also Odakyu Romancecar is among your options to travel between Odawara and Tokyo; the east terminus is Shinjuku Station.

Dear Omototenshi,
Thank you so much for your very helpful reply. I apologize for my many spelling errors! I was in a rush and didn't read over my text before sending it. I have looked at the website for the app and will download it. We are departing from Koyto Station to Odawara Station in the morning of 12/26 and then continuing on 12/27 from Odawara Station to Tokyo Station. We would like to take the bullet/speed train to maximize our time in Tokyo.
I will keep you posted as to how I fare in reserving my seats!
Again thank you for your very helpful and detailed response.