Five railroad operators have Odawara Stations (with JR-East and JR-Central counted as two JR companies), which are located nearby.
http://www.jreast.co.jp/e/stations/e382.htmlOdakyu (Odawara Line) and Hakone Tozan Railway are jointed in Odawara, and they share the tracks and the gate there.
On the section Odawara -- Hakone-Yumoto, Hakone Tozan Railway is using train cars offered by Odakyu. (Maybe that has caused your confusion.)
There are some through trains (including Odakyu Romancecar trains) which run on both Odakyu Odawara Line and this Hakone Tozan Railway section.
The railroad route Odawara -- Hakone-Yumoto -- Gora belongs to Hakone Tozan Railway.
There is, however, no train available through the whole route.
Shuttle trains are running on each of the two sections until and after Hakone-Yumoto.
You can change trains in Hakone-Yumoto Station usually via the same platform.
http://www.hakone-tozan.co.jp/station/img/map/map_hakoneyumoto.gifI understand we can use JR pass from Tokyo to Odawara. Your JR gate in Odawara Station depends on whether you use Tokaido Shinkansen of JR-Central or Tokaido Line of JR-East.
When you start from Tokyo Metropolis, you can make this choice in either Tokyo Station or Shinagawa Station. When you use Tokaido Shinkansen of JR-Central from Tokyo Station, please make sure not to pass through a Shinkansen gate of JR-East. (In Shinagawa Station, there is no other Shinkansen line, so you can just follow signs and icons for Shinkansen.)
A typical icon for Tokaido Shinkansen has blue parts.
http://commons.wikimedia.org/wiki/File:Shinkansen_blue.pngI will then buy a Hakone Free Pass in Odawara. A Hakone Freepass is available at a ticket vending machine of Odakyu in Odawara Station.
http://www.odakyu.jp/english/traffic/howto/ticket/Or, you can purchase one in the branch office (Odawara Travel Center) of Odakyu Travel
(open on weekdays from 10:00 to 19:00, open on other days from 10:00 to 18:00),
which is located across the walkway from the Odakyu gate.
http://www.odakyu-travel.co.jp/common/images/logo.jpg